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Ping Liu Jianghao Wang Huabin Zhang Shunli Zhang Feng Chi 《Waves in Random and Complex Media》2020,30(2):216-240
ABSTRACTA coupled Alice–Bob modified Korteweg de-Vries (mKdV) system is established from the mKdV equation in this paper, which is nonlocal and suitable to model two-place entangled events. The Lax integrability of the coupled Alice–Bob mKdV system is proved by demonstrating three types of Lax pairs. By means of the truncated Painlevé expansion, auto-Bäcklund transformation of the coupled Alice–Bob mKdV system and Bäcklund transformation between the coupled Alice–Bob mKdV system and the Schwarzian mKdV equation are demonstrated. Nonlocal residual symmetries of the coupled Alice–Bob mKdV system are researched. To obtain localized Lie point symmetries of residual symmetries, the coupled Alice–Bob mKdV system is extended to a system consisting six equations. Calculation on the prolonged system shows that it is invariant under the scaling transformations, space-time translations, phase translations and Galilean translations. One-parameter group transformation and one-parameter subgroup invariant solutions are obtained. The consistent Riccati expansion (CRE) solvability of the coupled Alice–Bob mKdV system is proved and some interaction structures between soliton–cnoidal waves are obtained by CRE. Moreover, Jacobi periodic wave solutions, solitary wave solutions and singular solutions are obtained by elliptic function expansion and exponential function expansion. 相似文献
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Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation 下载免费PDF全文
<正>This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries(KdV) equation and a coupled modified Korteweg-de Vries(mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional.Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions. 相似文献
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《Physics letters. A》2020,384(19):126471
The coupled Korteweg-de Vries (cKdV) system, originally proposed by Hirota and Satsuma [1], modeling the interaction of two long waves evolving with different dispersion relations, is considered. Multisoliton solutions are explicitly found in the Hirota-Satsuma system by means of an extension of the direct method due to Hirota [2]. Such multisolitons are found to be a complete family of interacting classical solitons consisting of the trivial ones corresponding to the decoupled N-soliton solution of the KdV equation and the ones coupled to the M-cKdV solitons, here simply referred to as the classical (N, M)-soliton solutions which are N+M interacting solitons indeed. Explicit analytical solutions, expressed in terms of hyperbolic functions, are found for the (0, 1), (1, 1) and (0, 2) cases while the process to generate the general (N, M)-soliton solutions is systematically described in detail. In the particular scenario of the (1, 1)-soliton, a novel two-hump one-soliton solution is obtained when a negative prestressing is prescribed for one of the waves in the merging of the 1-KdV and 1-cKdV solitons. Special attention is emphasized to the phase shift for the (1, 1) and (0, 2) interaction cases to asymptotically get a particular remarkable long range interaction phenomenon. Finally, some numerical evolutions are also considered to illustrate the interaction dynamics of the multisolitons and the new two-hump soliton in the different situations considered. 相似文献
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<正>Prom the point of view of approximate symmetry,the modified Korteweg-de Vries-Burgers(mKdV-Burgers) equation with weak dissipation is investigated.The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV-Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived;thereby infinite series solutions and general formulae can be obtained.The obtained result shows that the zero-order similarity solution to the mKdV—Burgers equation satisfies the PainleveⅡequation.Also,at the level of travelling wave reduction,the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation.As an illustrative example,when the zero-order tanh profile solution is chosen as an initial approximate solution,physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation. 相似文献
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Luis A. Cisneros-Ake Hugo Parra Prado Diego Joselito López Villatoro R. Carretero-González 《Physics letters. A》2018,382(12):837-845
We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg–de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS–mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution. 相似文献
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New nonsingular positon, negaton and complexiton solutions for the coupled mKdV system are constructed by means of Darboux transformation with constant seed solution and given out both analytically and graphically. 相似文献
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A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations 下载免费PDF全文
A modified Korteweg-de Vries (mKdV) lattice is found to be also a discrete Korteweg-de Vries (KdV) equation. A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics. 相似文献