Pub Date : 2025-02-01DOI: 10.1016/j.physd.2024.134514
Shuxian Wang, Chuanzhong Li
Basing on the universal character of B-type (BUC) hierarchy, through periodic reduction, we derived the bilinear equations that have the generalized reduced Schur Q-functions as tau functions. This process achieves a reduction of the BUC hierarchy. We refer to the resulting system as a reduced BUC hierarchy. Subsequently, the algebraic structure of the reduced BUC hierarchy is studied from the perspective of representation theory. We do this by transforming the bilinear equations using the neutral fermionic language. It is a widely accepted fact that a tau-function is considered as a solution of the BUC hierarchy when and only when it can be decomposed into a shifted action between two tau functions of the BKP hierarchy. We utilize this relationship to discover a class of polynomial tau-functions after the reduction of the BUC hierarchy. Furthermore, we extend our previous results to the B-type generalized UC (BGUC) hierarchy and its reduction.
{"title":"Reductions on B-type universal character hierarchy","authors":"Shuxian Wang, Chuanzhong Li","doi":"10.1016/j.physd.2024.134514","DOIUrl":"10.1016/j.physd.2024.134514","url":null,"abstract":"<div><div>Basing on the universal character of B-type (BUC) hierarchy, through periodic reduction, we derived the bilinear equations that have the generalized reduced Schur Q-functions as tau functions. This process achieves a reduction of the BUC hierarchy. We refer to the resulting system as a reduced BUC hierarchy. Subsequently, the algebraic structure of the reduced BUC hierarchy is studied from the perspective of representation theory. We do this by transforming the bilinear equations using the neutral fermionic language. It is a widely accepted fact that a tau-function is considered as a solution of the BUC hierarchy when and only when it can be decomposed into a shifted action between two tau functions of the BKP hierarchy. We utilize this relationship to discover a class of polynomial tau-functions after the reduction of the BUC hierarchy. Furthermore, we extend our previous results to the B-type generalized UC (BGUC) hierarchy and its reduction.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134514"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.physd.2024.134465
Zhichao Ma , Jinhao Liang , Junxiang Xu
In this paper, we consider the dynamics of a ball elastically bouncing off an infinitely heavy plate. Suppose the plate periodically moves in vertical direction and the ball between impacts is only subjected to the force with quadratic potential , where is Diophantine. Without imposing any assumption on the motion of plate besides smoothness, we prove that the ball never goes to infinity. Comparing to previous works, we drop certain assumptions which are usually imposed on the motion of the plate to guarantee twist conditions. This result depends on the famed Herman’s Last Geometric Theorem, which is given by Herman no later than 1995 in his “Seminaire de Systemes Dynamiques” at the Universite Paris VII and also in his 1998 ICM address (Herman, 1998 [1]). Its proof is also provided by Fayad and Krikorian (Fayad and Krikorian, 2009 [2]) in 2009 and recently we obtained a slightly different version (Ma and Xu, 2023 [3]), which is more convenient for this physical model.
{"title":"Boundedness of bouncing balls in quadratic potentials","authors":"Zhichao Ma , Jinhao Liang , Junxiang Xu","doi":"10.1016/j.physd.2024.134465","DOIUrl":"10.1016/j.physd.2024.134465","url":null,"abstract":"<div><div>In this paper, we consider the dynamics of a ball elastically bouncing off an infinitely heavy plate. Suppose the plate periodically moves in vertical direction and the ball between impacts is only subjected to the force with quadratic potential <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, where <span><math><msup><mrow><mrow><mo>(</mo><mn>4</mn><mi>α</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> is Diophantine. Without imposing any assumption on the motion of plate besides smoothness, we prove that the ball never goes to infinity. Comparing to previous works, we drop certain assumptions which are usually imposed on the motion of the plate to guarantee twist conditions. This result depends on the famed Herman’s Last Geometric Theorem, which is given by Herman no later than 1995 in his “Seminaire de Systemes Dynamiques” at the Universite Paris VII and also in his 1998 ICM address (Herman, 1998 <span><span>[1]</span></span>). Its proof is also provided by Fayad and Krikorian (Fayad and Krikorian, 2009 <span><span>[2]</span></span>) in 2009 and recently we obtained a slightly different version (Ma and Xu, 2023 <span><span>[3]</span></span>), which is more convenient for this physical model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134465"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.physd.2025.134527
Steffy Sara Varghese , Kuldeep Singh , Frank Verheest , Ioannis Kourakis
Various types of nonlinear partial-differential equations (PDEs) have been proposed in relation with plasma dynamics. In a 1D geometry, a Korteweg–de Vries (KdV) equation can be derived from a plasma fluid model for electrostatic excitations, by means of the reductive perturbation technique proposed by Taniuti and coworkers in the 1960s (Washimi and Taniuti, 1966). In the simplest “textbook level” case of an electron–ion plasma, describing an ion fluid evolving against an electron distribution (assumed known), this integrable equation, incorporating a nonlinearity coefficient (say, ) and a dispersion coefficient (), possesses analytical soliton solutions, whose polarity depends on the sign of . In more elaborate plasma configurations, including a (one, or more) (negatively charged) secondary ion or/and electron population(s), a critical plasma composition where the quadratic nonlinearity term A is negligible may be possible: in this case, a modified KdV (mKdV) equation may be derived, where dispersion is balanced by a cubic nonlinearity term, leading to exact pulse-shaped soliton solutions. A third possible scenario occurs when, depending on the relative concentration between positive and negative ions in the plasma mixture, an extended KdV (i.e. a Gardner) equation may be obtained, allowing for both positive and negative soliton solutions.
In this study, we have revisited the reductive perturbation technique, using a generic bi-fluid (electronegative plasma) model as starting point, in an effort to elucidate the subtleties underlying the reduction of a fluid plasma model to a nonlinear evolution equation for the electrostatic (ES) potential. Considering different plasma compositions, different types of PDEs have been obtained, in specific regimes. We have thus studied the conditions for the existence of various types of pulse-shaped excitations (solitary waves) for the electrostatic potential, associated with bipolar electric field () waveforms, such as the ones observed in planetary magnetospheres and in laboratory experiments.
{"title":"Integrable nonlinear PDEs as evolution equations derived from multi-ion fluid plasma models","authors":"Steffy Sara Varghese , Kuldeep Singh , Frank Verheest , Ioannis Kourakis","doi":"10.1016/j.physd.2025.134527","DOIUrl":"10.1016/j.physd.2025.134527","url":null,"abstract":"<div><div>Various types of nonlinear partial-differential equations (PDEs) have been proposed in relation with plasma dynamics. In a 1D geometry, a Korteweg–de Vries (KdV) equation can be derived from a plasma fluid model for electrostatic excitations, by means of the reductive perturbation technique proposed by Taniuti and coworkers in the 1960s (Washimi and Taniuti, 1966). In the simplest “textbook level” case of an electron–ion plasma, describing an ion fluid evolving against an electron distribution (assumed known), this integrable equation, incorporating a nonlinearity coefficient (say, <span><math><mi>A</mi></math></span>) and a dispersion coefficient (<span><math><mi>B</mi></math></span>), possesses analytical soliton solutions, whose polarity depends on the sign of <span><math><mi>A</mi></math></span>. In more elaborate plasma configurations, including a (one, or more) (negatively charged) secondary ion or/and electron population(s), a critical plasma composition where the quadratic nonlinearity term A is negligible may be possible: in this case, a modified KdV (mKdV) equation may be derived, where dispersion is balanced by a cubic nonlinearity term, leading to exact pulse-shaped soliton solutions. A third possible scenario occurs when, depending on the relative concentration between positive and negative ions in the plasma mixture, an extended KdV (i.e. a Gardner) equation may be obtained, allowing for both positive and negative soliton solutions.</div><div>In this study, we have revisited the reductive perturbation technique, using a generic bi-fluid (electronegative plasma) model as starting point, in an effort to elucidate the subtleties underlying the reduction of a fluid plasma model to a nonlinear evolution equation for the electrostatic (ES) potential. Considering different plasma compositions, different types of PDEs have been obtained, in specific regimes. We have thus studied the conditions for the existence of various types of pulse-shaped excitations (solitary waves) for the electrostatic potential, associated with bipolar electric field (<span><math><mrow><mi>E</mi><mo>=</mo><mo>−</mo><mfrac><mrow><mi>∂</mi><mi>ϕ</mi></mrow><mrow><mi>∂</mi><mi>x</mi></mrow></mfrac></mrow></math></span>) waveforms, such as the ones observed in planetary magnetospheres and in laboratory experiments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134527"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.physd.2025.134541
Truong X. Tran, Thau X. Nguyen
- We systematically investigate the generation of one-dimensional (1D) Jackiw–Rebbi (JR) states and 1D trivial localized states in interfaced binary waveguide arrays in both the linear and nonlinear regimes of Kerr type, respectively, from phase-modified and conventional Gaussian input beams; or even from two-point input beams. Our results show that Gaussian input beams and simple two-point input beams can efficiently generate JR states and trivial localized states with the conversion efficiency reaching around 90% and 70%, respectively. Right after launching these input beams into the interfaced BWAs, the re-distribution of the beam takes place where most energy of the beams is self-adjusted towards the right profiles of the JR states or trivial localized states, and only one small part of the input beam energy is lost as the weak radiation emitted towards two edges of the interfaced binary waveguide arrays.
{"title":"Generation of 1D Jackiw–Rebbi states and trivial localized states from simple input beams in interfaced binary waveguide arrays","authors":"Truong X. Tran, Thau X. Nguyen","doi":"10.1016/j.physd.2025.134541","DOIUrl":"10.1016/j.physd.2025.134541","url":null,"abstract":"<div><div>- We systematically investigate the generation of one-dimensional (1D) Jackiw–Rebbi (JR) states and 1D trivial localized states in interfaced binary waveguide arrays in both the linear and nonlinear regimes of Kerr type, respectively, from phase-modified and conventional Gaussian input beams; or even from two-point input beams. Our results show that Gaussian input beams and simple two-point input beams can efficiently generate JR states and trivial localized states with the conversion efficiency reaching around 90% and 70%, respectively. Right after launching these input beams into the interfaced BWAs, the re-distribution of the beam takes place where most energy of the beams is self-adjusted towards the right profiles of the JR states or trivial localized states, and only one small part of the input beam energy is lost as the weak radiation emitted towards two edges of the interfaced binary waveguide arrays.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134541"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.physd.2024.134468
Jian Song , Carlo R. Laing , Shenquan Liu
Interactions among many populations are common in both biological and engineering networks. This paper investigates the dynamics of a multi-population network composed of identical theta neurons, where each population has an infinite number of neurons. These neural oscillators are globally interconnected by pulse-like synapses whose sensitivity is adjustable. In this paper, the analytical technique developed by Ott–Antonsen is employed to streamline the dynamics of a large-scale network into a small set of variables and parameters, thereby representing the network’s overall state. The investigation indicates that our network can display either symmetric or asymmetric states. Meanwhile, an analysis of bifurcations with codimension-1 and -2 is conducted to examine the origins of the network’s multistability, oscillations, and hysteresis. Particular attention is paid to the influence of various network components, such as coupling patterns and population size. The analysis results reveal a strong correlation between multistability and the presence of a supercritical Hopf bifurcation with an attractive manifold. The evaluation procedure demonstrates the important role of balanced coupling in regulating the overall macroscopic dynamics of the network. Additionally, extensive testing suggests that networks with instantaneous synapses can exhibit asymmetric states even with homogeneous inter-population coupling, and this type of synapse removes Hopf bifurcations in two-population bifurcation scenarios. In three-population setups, there are subcritical Hopf bifurcations with an attractive manifold, leading to oscillations within specific parameter ranges. Our study provides new insights into the collective dynamics of neuronal nuclei in similar basal ganglia structures.
{"title":"A dynamical analysis of collective behavior in a multi-population network with infinite theta neurons","authors":"Jian Song , Carlo R. Laing , Shenquan Liu","doi":"10.1016/j.physd.2024.134468","DOIUrl":"10.1016/j.physd.2024.134468","url":null,"abstract":"<div><div>Interactions among many populations are common in both biological and engineering networks. This paper investigates the dynamics of a multi-population network composed of identical theta neurons, where each population has an infinite number of neurons. These neural oscillators are globally interconnected by pulse-like synapses whose sensitivity is adjustable. In this paper, the analytical technique developed by Ott–Antonsen is employed to streamline the dynamics of a large-scale network into a small set of variables and parameters, thereby representing the network’s overall state. The investigation indicates that our network can display either symmetric or asymmetric states. Meanwhile, an analysis of bifurcations with codimension-1 and -2 is conducted to examine the origins of the network’s multistability, oscillations, and hysteresis. Particular attention is paid to the influence of various network components, such as coupling patterns and population size. The analysis results reveal a strong correlation between multistability and the presence of a supercritical Hopf bifurcation with an attractive manifold. The evaluation procedure demonstrates the important role of balanced coupling in regulating the overall macroscopic dynamics of the network. Additionally, extensive testing suggests that networks with instantaneous synapses can exhibit asymmetric states even with homogeneous inter-population coupling, and this type of synapse removes Hopf bifurcations in two-population bifurcation scenarios. In three-population setups, there are subcritical Hopf bifurcations with an attractive manifold, leading to oscillations within specific parameter ranges. Our study provides new insights into the collective dynamics of neuronal nuclei in similar basal ganglia structures.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134468"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.physd.2024.134454
Olga S. Rozanova
We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler–Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equilibrium to determine which properties of the doping profile contribute to the blow-up. We also propose a numerical procedure that allows one to find the blow-up time for any initial data and present examples of such calculations for various doping profiles for standard initial data, corresponding to the laser pulse.
{"title":"The repulsive Euler–Poisson equations with variable doping profile","authors":"Olga S. Rozanova","doi":"10.1016/j.physd.2024.134454","DOIUrl":"10.1016/j.physd.2024.134454","url":null,"abstract":"<div><div>We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler–Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equilibrium to determine which properties of the doping profile contribute to the blow-up. We also propose a numerical procedure that allows one to find the blow-up time for any initial data and present examples of such calculations for various doping profiles for standard initial data, corresponding to the laser pulse.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134454"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-30DOI: 10.1016/j.physd.2024.134521
Alon Drory
I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the Lagrangian a term containing auxiliary variables. As a proof of concept, I apply this representation to the three-body problem with a generalized potential that depends on the distance between the bodies as . I obtain the equilateral and collinear solutions (corresponding to the Lagrange and Euler solutions if ) in a particularly simple way. In the collinear solution, this representation leads to several new bounds on the relative distances of the bodies.
{"title":"Pair space in classical mechanics, I: The three-body problem","authors":"Alon Drory","doi":"10.1016/j.physd.2024.134521","DOIUrl":"10.1016/j.physd.2024.134521","url":null,"abstract":"<div><div>I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the Lagrangian a term containing auxiliary variables. As a proof of concept, I apply this representation to the three-body problem with a generalized potential that depends on the distance <span><math><mi>r</mi></math></span> between the bodies as <span><math><msup><mrow><mi>r</mi></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup></math></span>. I obtain the equilateral and collinear solutions (corresponding to the Lagrange and Euler solutions if <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>) in a particularly simple way. In the collinear solution, this representation leads to several new bounds on the relative distances of the bodies.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134521"},"PeriodicalIF":2.7,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper aims to explore the relations between the Sylvester equation and semi-discrete integrable systems. Starting from the Sylvester equation , the semi-discrete Toda equation, the modified semi-discrete Toda equation and their discrete Miura transformation are constructed by Cauchy matrix approach in a systematic way. Lax pair is derived for the modified semi-discrete Toda equation. Explicit solutions are presented for the semi-discrete Toda equation and classified according to the canonical forms of the constant matrices and . As examples, soliton solutions and multi-pole solutions are analyzed and illustrated. The connection of the function of the semi-discrete Toda equation with Cauchy matrix approach is clarified. Under the constraint , the semi-discrete sine-Gordon equation, the modified semi-discrete sine-Gordon equation and their discrete Miura transformation are obtained, which can also be treated as the two-periodic reductions of the corresponding results of the semi-discrete Toda system. Integrable properties including the bilinear form, Lax pair and various types of solutions are investigated for the semi-discrete sine-Gordon equation. In particular, kink solutions and breathers of the semi-discrete sine-Gordon equation are analyzed and their dynamical behaviors are illustrated.
{"title":"Cauchy matrix scheme and the semi-discrete Toda and sine-Gordon systems","authors":"Tong Shen , Chunxia Li , Xinyuan Zhang , Songlin Zhao , Zhen Zhou","doi":"10.1016/j.physd.2025.134543","DOIUrl":"10.1016/j.physd.2025.134543","url":null,"abstract":"<div><div>This paper aims to explore the relations between the Sylvester equation and semi-discrete integrable systems. Starting from the Sylvester equation <span><math><mrow><mi>K</mi><mi>M</mi><mo>+</mo><mi>M</mi><mi>L</mi><mo>=</mo><mi>r</mi><msup><mrow><mi>s</mi></mrow><mrow><mo>⊤</mo></mrow></msup></mrow></math></span>, the semi-discrete Toda equation, the modified semi-discrete Toda equation and their discrete Miura transformation are constructed by Cauchy matrix approach in a systematic way. Lax pair is derived for the modified semi-discrete Toda equation. Explicit solutions are presented for the semi-discrete Toda equation and classified according to the canonical forms of the constant matrices <span><math><mi>K</mi></math></span> and <span><math><mi>L</mi></math></span>. As examples, soliton solutions and multi-pole solutions are analyzed and illustrated. The connection of the <span><math><mi>τ</mi></math></span> function of the semi-discrete Toda equation with Cauchy matrix approach is clarified. Under the constraint <span><math><mrow><mi>K</mi><mo>=</mo><mi>L</mi></mrow></math></span>, the semi-discrete sine-Gordon equation, the modified semi-discrete sine-Gordon equation and their discrete Miura transformation are obtained, which can also be treated as the two-periodic reductions of the corresponding results of the semi-discrete Toda system. Integrable properties including the bilinear form, Lax pair and various types of solutions are investigated for the semi-discrete sine-Gordon equation. In particular, kink solutions and breathers of the semi-discrete sine-Gordon equation are analyzed and their dynamical behaviors are illustrated.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134543"},"PeriodicalIF":2.7,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-29DOI: 10.1016/j.physd.2025.134555
Roberto Bistel , Ana Amador , Gabriel B. Mindlin
Until the spread of digital recording technology, our knowledge of the history of avian vocal culture was based on onomatopoeic descriptions or notations inspired by musical notation. In the 1960s, hand-drawn annotations of the frequency modulations in the songs of Rufous-collared sparrows (Zonotrichia capensis) were made in a natural reserve in Argentina. Some of these song themes have been preserved to the present day, while others have not appeared in recent recordings. In this work, we used a dynamical system based on an avian vocal production model to generate synthetic songs. We designed a song that matches the description of a currently absent theme and used it as a vocal tutor for wild juveniles. The success of our approach suggests a promising tool for preserving the vocal repertoire of wild birds.
{"title":"Conservation of avian vocal heritage through synthetic song reintroduction","authors":"Roberto Bistel , Ana Amador , Gabriel B. Mindlin","doi":"10.1016/j.physd.2025.134555","DOIUrl":"10.1016/j.physd.2025.134555","url":null,"abstract":"<div><div>Until the spread of digital recording technology, our knowledge of the history of avian vocal culture was based on onomatopoeic descriptions or notations inspired by musical notation. In the 1960s, hand-drawn annotations of the frequency modulations in the songs of Rufous-collared sparrows (<em>Zonotrichia capensis</em>) were made in a natural reserve in Argentina. Some of these song themes have been preserved to the present day, while others have not appeared in recent recordings. In this work, we used a dynamical system based on an avian vocal production model to generate synthetic songs. We designed a song that matches the description of a currently absent theme and used it as a vocal tutor for wild juveniles. The success of our approach suggests a promising tool for preserving the vocal repertoire of wild birds.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134555"},"PeriodicalIF":2.7,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1016/j.physd.2024.134455
Amit Anand , Robert B. Mann , Shohini Ghose
Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic behavior in its classical limit: the kicked top model, whose classical dynamics are governed by Hamilton’s equations on phase space, whereas its quantum dynamics are described by the Schrödinger equation in Hilbert space. We explore the critical degree of non-linearity signifying the onset of chaos in the kicked top by modifying the original Hamiltonian so that the non-linearity is parameterized by a quantity . We find two distinct behaviors of the modified kicked top depending on the value of . Chaos intensifies as varies within the range of , whereas it diminishes for , eventually transitioning to a purely regular oscillating system as tends to infinity. We also comment on the complicated phase space structure for non-chaotic dynamics. Our investigation sheds light on the relationship between non-linearity and chaos in classical systems, offering insights into their dynamical behavior.
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