The quasi-periodic solutions for the supersymmetric variable-coefficient KdV equation

2020 ◽  
Vol 34 (16) ◽  
pp. 2050171
Author(s):  
Chao Dong ◽  
Shu-Fang Deng
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Singularity Analysis ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Painlevé Property ◽  
Hirota Bilinear

The supersymmetric variable-coefficient KdV equation is presented and it admits Painlevé property by the standard singularity analysis. Based on Hirota bilinear method and Riemann theta function, one and two quasi-periodic wave solutions for the supersymmetric variable-coefficient KdV equation are studied. In addition, we give the asymptotic relations between quasi-periodic wave solutions and soliton solutions.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

Constructing Quasi-Periodic Wave Solutions of Differential-Difference Equation by Hirota Bilinear Method

2016 ◽  
Vol 71 (12) ◽  
pp. 1159-1165
Author(s):  
Qi Wang
Keyword(s):  
Difference Equation ◽  
Wave Solution ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solution ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Differential Difference Equation ◽  
Hirota Bilinear

AbstractIn the present paper, based on the Riemann theta function, the Hirota bilinear method is extended to directly construct a kind of quasi-periodic wave solution of a new integrable differential-difference equation. The asymptotic property of the quasi-periodic wave solution is analyzed in detail. It will be shown that quasi-periodic wave solution converge to the soliton solutions under certain conditions and small amplitude limit.

On quasi-periodic wave solutions and asymptotic behaviors to a (2 + 1)-dimensional generalized variable-coefficient Sawada–Kotera equation

2015 ◽  
Vol 29 (19) ◽  
pp. 1550101 ◽  
Author(s):  
Jian-Min Tu ◽  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Pan-Li Ma
Keyword(s):  
Periodic Solutions ◽  
Variable Coefficient ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Bell Polynomials ◽  
Nonlinear Phenomena ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Bilinear Equation

In this paper, a [Formula: see text]-dimensional generalized variable-coefficient Sawada–Kotera (gvcSK) equation is investigated, which describes many nonlinear phenomena in fluid dynamics and plasma physics. Based on the properties of binary Bell polynomials, we present a Hirota’s bilinear equation to the gvcSK equation. By virtue of the Hirota’s bilinear equation, we obtain the N-soliton solutions and the quasi-periodic wave solutions of the gvcSK equation, which can be reduced to the ones of several integrable equations such as Sawada–Kotera, modified Caudrey–Dodd–Gibbon–Sawada–Kotera, isospectral BKP equations and etc. Furthermore, we obtain the relationship between the soliton solutions and periodic solutions by considering the asymptotic properties of the periodic solutions.

Construction of Quasi-Periodic Wave Solutions for Differential- Difference Equation

2012 ◽  
Vol 67 (1-2) ◽  
pp. 21-28 ◽  
Author(s):  
Y. C. Hon ◽  
Qi Wang
Keyword(s):  
Difference Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Constructive Method ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Equation Analysis ◽  
Differential Difference Equation ◽  
Generalized Differential

Based on the use of the Hirota bilinear method and the Riemann theta function, we develop in this paper a constructive method for obtaining explicit quasi-periodic wave solutions of a new integrable generalized differential-difference equation. Analysis on the asymptotic property of the quasiperiodic wave solutions is given, and it is shown that the quasi-periodic wave solutions converge to the soliton solutions under certain conditions.

Integrability and Multi-Soliton Solutions for a Variable-Coefficient Coupled Gross–Pitaevskii System for Atomic MatterWaves

2012 ◽  
Vol 67 (10-11) ◽  
pp. 525-533
Author(s):  
Zhi-Qiang Lin ◽  
Bo Tian ◽  
Ming Wang ◽  
Xing Lu
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Einstein Condensate ◽  
Matter Wave ◽  
Bilinear Method ◽  
Matter Waves ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Hirota Bilinear

Under investigation in this paper is a variable-coefficient coupled Gross-Pitaevskii (GP) system, which is associated with the studies on atomic matter waves. Through the Painlev´e analysis, we obtain the constraint on the variable coefficients, under which the system is integrable. The bilinear form and multi-soliton solutions are derived with the Hirota bilinear method and symbolic computation. We found that: (i) in the elastic collisions, an external potential can change the propagation of the soliton, and thus the density of the matter wave in the two-species Bose-Einstein condensate (BEC); (ii) in the shape-changing collision, the solitons can exchange energy among different species, leading to the change of soliton amplitudes.We also present the collisions among three solitons of atomic matter waves.

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

2021 ◽  
Author(s):  
Lingchao He ◽  
Jianwen Zhang ◽  
Zhonglong Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Water Waves ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Before And After

Abstract In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Periodic Wave Solutions ◽  
Wave Solutions

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

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