{"title":"DNLS 方程的暗孤子沿大尺度背景传播","authors":"A.M. Kamchatnov, D.V. Shaykin","doi":"10.1016/j.wavemoti.2024.103349","DOIUrl":null,"url":null,"abstract":"<div><p>We study dynamics of dark solitons in the theory of the derivative nonlinear Schrödinger equations by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes’ remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet’s wave number <span><math><mi>k</mi></math></span> by <span><math><mrow><mi>i</mi><mi>κ</mi></mrow></math></span>, <span><math><mi>κ</mi></math></span> being the soliton’s inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton’s motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the Kaup-Newell DNLS equation.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"129 ","pages":"Article 103349"},"PeriodicalIF":2.1000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Propagation of dark solitons of DNLS equations along a large-scale background\",\"authors\":\"A.M. Kamchatnov, D.V. Shaykin\",\"doi\":\"10.1016/j.wavemoti.2024.103349\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study dynamics of dark solitons in the theory of the derivative nonlinear Schrödinger equations by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes’ remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet’s wave number <span><math><mi>k</mi></math></span> by <span><math><mrow><mi>i</mi><mi>κ</mi></mrow></math></span>, <span><math><mi>κ</mi></math></span> being the soliton’s inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton’s motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the Kaup-Newell DNLS equation.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"129 \",\"pages\":\"Article 103349\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524000799\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524000799","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
Propagation of dark solitons of DNLS equations along a large-scale background
We study dynamics of dark solitons in the theory of the derivative nonlinear Schrödinger equations by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes’ remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet’s wave number by , being the soliton’s inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton’s motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the Kaup-Newell DNLS equation.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.