We revisit here the dynamics of an engineered dimer granular crystal under an external periodic drive in the presence of dissipation. Earlier findings included a saddle-node bifurcation, whose terminal point initiated the observation of chaos; the system was found to exhibit bistability and potential quasiperiodicity. We now complement these findings by the identification of unstable manifolds of saddle periodic solutions (saddle points of the stroboscopic map) within the system dynamics. We unravel how homoclinic tangles of these manifolds lead to the appearance of a chaotic attractor, upon the apparent period-doubling bifurcations that destroy invariant tori associated with quasiperiodicity. These findings complement the earlier ones, offering more concrete insights into the emergence of chaos within this high-dimensional, experimentally accessible system.
{"title":"Global Bifurcations in a Damped-Driven Diatomic Granular Crystal","authors":"D. Pozharskiy, I. G. Kevrekidis, P. G. Kevrekidis","doi":"arxiv-2407.19347","DOIUrl":"https://doi.org/arxiv-2407.19347","url":null,"abstract":"We revisit here the dynamics of an engineered dimer granular crystal under an\u0000external periodic drive in the presence of dissipation. Earlier findings\u0000included a saddle-node bifurcation, whose terminal point initiated the\u0000observation of chaos; the system was found to exhibit bistability and potential\u0000quasiperiodicity. We now complement these findings by the identification of\u0000unstable manifolds of saddle periodic solutions (saddle points of the\u0000stroboscopic map) within the system dynamics. We unravel how homoclinic tangles\u0000of these manifolds lead to the appearance of a chaotic attractor, upon the\u0000apparent period-doubling bifurcations that destroy invariant tori associated\u0000with quasiperiodicity. These findings complement the earlier ones, offering\u0000more concrete insights into the emergence of chaos within this\u0000high-dimensional, experimentally accessible system.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The compacton, peakon, and Burgers-Hopf equations regularized by the Galerkin truncation preserving finite Fourier modes are found to support new travelling waves and interacting solitonic structures amidst weaker less-ordered components (`longons'). Different perspectives focusing on the zero-Hamiltonian solitonic, chaotic-looking, and stationary longons are also offered.
{"title":"Solitary Waves and Interacting Longons in Galerkin-truncated Systems","authors":"Jian-Zhou Zhu","doi":"arxiv-2407.20277","DOIUrl":"https://doi.org/arxiv-2407.20277","url":null,"abstract":"The compacton, peakon, and Burgers-Hopf equations regularized by the Galerkin\u0000truncation preserving finite Fourier modes are found to support new travelling\u0000waves and interacting solitonic structures amidst weaker less-ordered\u0000components (`longons'). Different perspectives focusing on the zero-Hamiltonian\u0000solitonic, chaotic-looking, and stationary longons are also offered.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"197 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Avinash Khare, Fred Cooper, John F. Dawson, Efstathios G. Charalampidis, Avadh Saxena
Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the coupled massive Thirring and the coupled Soler model to arbitrary nonlinear parameter $kappa$ and obtain exact solitary wave solutions in both cases. Remarkably, it turns out that in both the models, because of the conservation laws of charge and energy, the exact solutions we find seem to not depend on how we parameterize them, and the charge density of these solutions is related to the charge density of the single field solutions found earlier by a subset of the present authors. In both the models, a nonrelativistic reduction of the equations leads to the same conclusion that the solutions are proportional to those found in the one component field case.
{"title":"Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity","authors":"Avinash Khare, Fred Cooper, John F. Dawson, Efstathios G. Charalampidis, Avadh Saxena","doi":"arxiv-2407.16596","DOIUrl":"https://doi.org/arxiv-2407.16596","url":null,"abstract":"Motivated by the recent introduction of an integrable coupled massive\u0000Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model.\u0000Further we generalize both the coupled massive Thirring and the coupled Soler\u0000model to arbitrary nonlinear parameter $kappa$ and obtain exact solitary wave\u0000solutions in both cases. Remarkably, it turns out that in both the models,\u0000because of the conservation laws of charge and energy, the exact solutions we\u0000find seem to not depend on how we parameterize them, and the charge density of\u0000these solutions is related to the charge density of the single field solutions\u0000found earlier by a subset of the present authors. In both the models, a\u0000nonrelativistic reduction of the equations leads to the same conclusion that\u0000the solutions are proportional to those found in the one component field case.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a computational study of the pairwise interactions between defects in the recently introduced non-reciprocal Cahn-Hilliard model. The evolution of a defect pair exhibits dependence upon their corresponding topological charges, initial separation, and the non-reciprocity coupling constant $alpha$. We find that the stability of isolated topologically neutral targets significantly affects the pairwise defect interactions. At large separations, defect interactions are negligible and a defect pair is stable. When positioned in relatively close proximity, a pair of oppositely charged spirals or targets merge to form a single target. At low $alpha$, like-charged spirals form rotating bound pairs, which are however torn apart by spontaneously formed targets at high $alpha$. Similar preference for charged or neutral solutions is also seen for a spiral target pair where the spiral dominates at low $alpha$, but concedes to the target at large $alpha$. Our work sheds light on the complex phenomenology of non-reciprocal active matter systems when their collective dynamics involves topological defects.
{"title":"Defect interactions in the non-reciprocal Cahn-Hilliard model","authors":"Navdeep Rana, Ramin Golestanian","doi":"arxiv-2407.16547","DOIUrl":"https://doi.org/arxiv-2407.16547","url":null,"abstract":"We present a computational study of the pairwise interactions between defects\u0000in the recently introduced non-reciprocal Cahn-Hilliard model. The evolution of\u0000a defect pair exhibits dependence upon their corresponding topological charges,\u0000initial separation, and the non-reciprocity coupling constant $alpha$. We find\u0000that the stability of isolated topologically neutral targets significantly\u0000affects the pairwise defect interactions. At large separations, defect\u0000interactions are negligible and a defect pair is stable. When positioned in\u0000relatively close proximity, a pair of oppositely charged spirals or targets\u0000merge to form a single target. At low $alpha$, like-charged spirals form\u0000rotating bound pairs, which are however torn apart by spontaneously formed\u0000targets at high $alpha$. Similar preference for charged or neutral solutions\u0000is also seen for a spiral target pair where the spiral dominates at low\u0000$alpha$, but concedes to the target at large $alpha$. Our work sheds light on\u0000the complex phenomenology of non-reciprocal active matter systems when their\u0000collective dynamics involves topological defects.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gino Biondini, Gennady A. El, Xu-Dan Luo Jeffrey Oregero, Alexander Tovbis
We present an analytical model of integrable turbulence in the focusing nonlinear Schr"odinger (fNLS) equation, generated by a one-parameter family of finite-band elliptic potentials in the semiclassical limit. We show that the spectrum of these potentials exhibits a thermodynamic band/gap scaling compatible with that of soliton and breather gases depending on the value of the elliptic parameter m of the potential. We then demonstrate that, upon augmenting the potential by a small random noise (which is inevitably present in real physical systems), the solution of the fNLS equation evolves into a fully randomized, spatially homogeneous breather gas, a phenomenon we call breather gas fission. We show that the statistical properties of the breather gas at large times are determined by the spectral density of states generated by the unperturbed initial potential. We analytically compute the kurtosis of the breather gas as a function of the elliptic parameter m, and we show that it is greater than 2 for all non-zero m, implying non-Gaussian statistics. Finally, we verify the theoretical predictions by comparison with direct numerical simulations of the fNLS equation. These results establish a link between semiclassical limits of integrable systems and the statistical characterization of their soliton and breather gases.
我们提出了聚焦非线性薛定谔方程（fNLS）中可积分湍流的分析模型，该模型是由半经典极限中无穷带椭圆势的一参数族产生的。我们证明，这些势的频谱表现出与孤子和呼吸气体相匹配的热力学带/隙缩放，这取决于势的椭圆参数 m 的值。然后我们证明，在用小的随机噪声（这在实际物理系统中不可避免地存在）增强势时，fNLS方程的解会演变成完全随机的、空间均匀的呼吸气体，我们称这种现象为呼吸气体裂变。我们证明，呼吸气体在大时间内的统计特性是由未扰动初始势产生的状态谱密度决定的。我们分析计算了作为椭圆参数 m 函数的呼吸气体峰度，结果表明，对于所有非零 m，峰度都大于 2，这意味着非高斯统计。这些结果在可积分系统的半经典极限与其孤子和呼吸气体的统计特性之间建立了联系。
{"title":"Breather gas fission from elliptic potentials in self-focusing media","authors":"Gino Biondini, Gennady A. El, Xu-Dan Luo Jeffrey Oregero, Alexander Tovbis","doi":"arxiv-2407.15758","DOIUrl":"https://doi.org/arxiv-2407.15758","url":null,"abstract":"We present an analytical model of integrable turbulence in the focusing\u0000nonlinear Schr\"odinger (fNLS) equation, generated by a one-parameter family of\u0000finite-band elliptic potentials in the semiclassical limit. We show that the\u0000spectrum of these potentials exhibits a thermodynamic band/gap scaling\u0000compatible with that of soliton and breather gases depending on the value of\u0000the elliptic parameter m of the potential. We then demonstrate that, upon\u0000augmenting the potential by a small random noise (which is inevitably present\u0000in real physical systems), the solution of the fNLS equation evolves into a\u0000fully randomized, spatially homogeneous breather gas, a phenomenon we call\u0000breather gas fission. We show that the statistical properties of the breather\u0000gas at large times are determined by the spectral density of states generated\u0000by the unperturbed initial potential. We analytically compute the kurtosis of\u0000the breather gas as a function of the elliptic parameter m, and we show that it\u0000is greater than 2 for all non-zero m, implying non-Gaussian statistics.\u0000Finally, we verify the theoretical predictions by comparison with direct\u0000numerical simulations of the fNLS equation. These results establish a link\u0000between semiclassical limits of integrable systems and the statistical\u0000characterization of their soliton and breather gases.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the radiation in kink collision via a model that varies between $phi^6$ theory and $phi^2$ theory with some discontinuities. Both numerical and analytical methods were used to investigate The kink-antikink(KAK) and antikink-kink(AKK) collision. In the numerical analysis, we found the critical velocities in both collisions increased with $n$. We also found a finite lifetime oscillon window in KAK collision for $n=2$. In the analytical part, we found a family of shock wave solutions that describes radiation in the kink collision perfectly. Moreover, an analytical AKK solution at $nrightarrowinfty$ and $v=1$ was found by considering a certain limit of these solutions.
我们通过一个介于$phi^6$理论和$phi^2$理论之间并带有一些不连续性的模型来研究扭结碰撞中的辐射。我们采用数值方法和分析方法研究了 "扭结-反扭结（KAK）"和 "反扭结-扭结（AKK）"碰撞。在数值分析中，我们发现这两种碰撞的临界值都随 $n$ 的增大而增大。我们还发现，在KAK碰撞中，当n=2时，会出现一个有限寿命的振荡窗口。在分析部分，我们发现了一个冲击波解族，它能完美地描述 KK 碰撞中的辐射。此外，通过考虑这些解的某个极限，我们发现了在$nrightarrowinfty$ 和 $v=1$时的AKK分析解。
{"title":"Radiation-like Shock Waves in Kink Scattering","authors":"Xiang Li, Lingxiao Long","doi":"arxiv-2407.14479","DOIUrl":"https://doi.org/arxiv-2407.14479","url":null,"abstract":"We study the radiation in kink collision via a model that varies between\u0000$phi^6$ theory and $phi^2$ theory with some discontinuities. Both numerical\u0000and analytical methods were used to investigate The kink-antikink(KAK) and\u0000antikink-kink(AKK) collision. In the numerical analysis, we found the critical\u0000velocities in both collisions increased with $n$. We also found a finite\u0000lifetime oscillon window in KAK collision for $n=2$. In the analytical part, we\u0000found a family of shock wave solutions that describes radiation in the kink\u0000collision perfectly. Moreover, an analytical AKK solution at\u0000$nrightarrowinfty$ and $v=1$ was found by considering a certain limit of\u0000these solutions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {bf 302}, 815-841 (2011)], establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such wave forms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the $phi^4$ model considered herein, the breather solutions are generically found to be unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially-heterogeneous, continuum nonlinear wave equation models.
{"title":"Stability of Breathers for a Periodic Klein-Gordon Equation","authors":"Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis","doi":"arxiv-2407.10766","DOIUrl":"https://doi.org/arxiv-2407.10766","url":null,"abstract":"The existence of breather type solutions, i.e., periodic in time,\u0000exponentially localized in space solutions, is a very unusual feature for\u0000continuum, nonlinear wave type equations. Following an earlier work [Comm.\u0000Math. Phys. {bf 302}, 815-841 (2011)], establishing a theorem for the\u0000existence of such structures, we bring to bear a combination of\u0000analysis-inspired numerical tools that permit the construction of such wave\u0000forms to a desired numerical accuracy. In addition, this enables us to explore\u0000their numerical stability. Our computations show that for the spatially\u0000heterogeneous form of the $phi^4$ model considered herein, the breather\u0000solutions are generically found to be unstable. Their instability seems to\u0000generically favor the motion of the relevant structures. We expect that these\u0000results may inspire further studies towards the identification of stable\u0000continuous breathers in spatially-heterogeneous, continuum nonlinear wave\u0000equation models.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. D'Ambroise, W. Wang, C. Ticknor, R. Carretero-González, P. G. Kevrekidis
The study of structures involving vortices in one component and bright solitary waves in another has a time-honored history in two-component atomic Bose-Einstein condensates. In the present work, we revisit this topic extending considerations well-past the near-integrable regime of nearly equal scattering lengths. Instead, we focus on stationary states and spectral stability of such structures for large values of the inter-component interaction coefficient. We find that the state can manifest dynamical instabilities for suitable parameter values. We also explore a phenomenological, yet quantitatively accurate upon suitable tuning, particle model which, in line also with earlier works, offers the potential of accurately following the associated stability and dynamical features. Finally, we probe the dynamics of the unstable vortex-bright structure, observing an unprecedented, to our knowledge, instability scenario in which the oscillatory instability leads to a patch of vorticity that harbors and eventually ejects multiple vortex-bright structures.
{"title":"Stability and dynamics of massive vortices in two-component Bose-Einstein condensates","authors":"J. D'Ambroise, W. Wang, C. Ticknor, R. Carretero-González, P. G. Kevrekidis","doi":"arxiv-2407.10324","DOIUrl":"https://doi.org/arxiv-2407.10324","url":null,"abstract":"The study of structures involving vortices in one component and bright\u0000solitary waves in another has a time-honored history in two-component atomic\u0000Bose-Einstein condensates. In the present work, we revisit this topic extending\u0000considerations well-past the near-integrable regime of nearly equal scattering\u0000lengths. Instead, we focus on stationary states and spectral stability of such\u0000structures for large values of the inter-component interaction coefficient. We\u0000find that the state can manifest dynamical instabilities for suitable parameter\u0000values. We also explore a phenomenological, yet quantitatively accurate upon\u0000suitable tuning, particle model which, in line also with earlier works, offers\u0000the potential of accurately following the associated stability and dynamical\u0000features. Finally, we probe the dynamics of the unstable vortex-bright\u0000structure, observing an unprecedented, to our knowledge, instability scenario\u0000in which the oscillatory instability leads to a patch of vorticity that harbors\u0000and eventually ejects multiple vortex-bright structures.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Futai Hu, Abhinav Kumar Vinod, Wenting Wang, Hsiao-Hsuan Chin, James F. McMillan, Ziyu Zhan, Yuan Meng, Mali Gong, Chee Wei Wong
Solitons, the distinct balance between nonlinearity and dispersion, provide a route toward ultrafast electromagnetic pulse shaping, high-harmonic generation, real-time image processing, and RF photonic communications. Here we newly explore and observe the spatio-temporal breather dynamics of optical soliton crystals in frequency microcombs, examining spatial breathers, chaos transitions, and dynamical deterministic switching in nonlinear measurements and theory. To understand the breather solitons, we describe their dynamical routes and two example transitional maps of the ensemble spatial breathers, with and without chaos initiation. We elucidate the physical mechanisms of the breather dynamics in the soliton crystal microcombs, in the interaction plane limit cycles and in the domain-wall understanding with parity symmetry breaking from third order dispersion. We present maps of the accessible nonlinear regions, the breather frequency dependences on third order dispersion and avoided mode crossing strengths, and the transition between the collective breather spatiotemporal states. Our range of measurements matches well with our first-principles theory and nonlinear modeling. To image these soliton ensembles and their breathers, we further constructed panoramic temporal imaging for simultaneous fast and slow axis two dimensional mapping of the breathers. In the phase differential sampling, we present two dimensional evolution maps of soliton crystal breathers, including with defects, in both stable breathers and breathers with drift. Our fundamental studies contribute to the understanding of nonlinear dynamics in soliton crystal complexes, their spatiotemporal dependences, and their stability-existence zones.
{"title":"Spatio-temporal breather dynamics in microcomb soliton crystals","authors":"Futai Hu, Abhinav Kumar Vinod, Wenting Wang, Hsiao-Hsuan Chin, James F. McMillan, Ziyu Zhan, Yuan Meng, Mali Gong, Chee Wei Wong","doi":"arxiv-2407.10213","DOIUrl":"https://doi.org/arxiv-2407.10213","url":null,"abstract":"Solitons, the distinct balance between nonlinearity and dispersion, provide a\u0000route toward ultrafast electromagnetic pulse shaping, high-harmonic generation,\u0000real-time image processing, and RF photonic communications. Here we newly\u0000explore and observe the spatio-temporal breather dynamics of optical soliton\u0000crystals in frequency microcombs, examining spatial breathers, chaos\u0000transitions, and dynamical deterministic switching in nonlinear measurements\u0000and theory. To understand the breather solitons, we describe their dynamical\u0000routes and two example transitional maps of the ensemble spatial breathers,\u0000with and without chaos initiation. We elucidate the physical mechanisms of the\u0000breather dynamics in the soliton crystal microcombs, in the interaction plane\u0000limit cycles and in the domain-wall understanding with parity symmetry breaking\u0000from third order dispersion. We present maps of the accessible nonlinear\u0000regions, the breather frequency dependences on third order dispersion and\u0000avoided mode crossing strengths, and the transition between the collective\u0000breather spatiotemporal states. Our range of measurements matches well with our\u0000first-principles theory and nonlinear modeling. To image these soliton\u0000ensembles and their breathers, we further constructed panoramic temporal\u0000imaging for simultaneous fast and slow axis two dimensional mapping of the\u0000breathers. In the phase differential sampling, we present two dimensional\u0000evolution maps of soliton crystal breathers, including with defects, in both\u0000stable breathers and breathers with drift. Our fundamental studies contribute\u0000to the understanding of nonlinear dynamics in soliton crystal complexes, their\u0000spatiotemporal dependences, and their stability-existence zones.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alina Barbara Steinberg, Fabian Maucher, Svetlana Gurevich, Uwe Thiele
We report the existence of localized states in dipolar Bose-Einstein condensates confined to a tubular geometry. We first perform a bifurcation analysis to track their emergence in a one-dimensional domain for numerical feasibility and find that localized states can become the ground state in suitable parameter regions. Their existence for parameters featuring a supercritical primary bifurcation shows that the latter is not sufficient to conclude that the phase transition is of second order, hence density modulations can jump rather than emerging gradually. Finally, we show that localized states also exist in a three-dimensional domain.
{"title":"Localized States in Dipolar Bose-Einstein Condensates: To be or not to be of second order","authors":"Alina Barbara Steinberg, Fabian Maucher, Svetlana Gurevich, Uwe Thiele","doi":"arxiv-2407.09177","DOIUrl":"https://doi.org/arxiv-2407.09177","url":null,"abstract":"We report the existence of localized states in dipolar Bose-Einstein\u0000condensates confined to a tubular geometry. We first perform a bifurcation\u0000analysis to track their emergence in a one-dimensional domain for numerical\u0000feasibility and find that localized states can become the ground state in\u0000suitable parameter regions. Their existence for parameters featuring a\u0000supercritical primary bifurcation shows that the latter is not sufficient to\u0000conclude that the phase transition is of second order, hence density\u0000modulations can jump rather than emerging gradually. Finally, we show that\u0000localized states also exist in a three-dimensional domain.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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