scholarly journals EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS

1999 ◽  
Vol 48 (11) ◽  
pp. 1957
Author(s):  
YAN ZHEN-YA ◽  
ZHANG HONG-QING
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Exact Soliton Solutions

Exact Soliton Solutions of the Variable Coefficient KdV Equation with Forced Term

2014 ◽  
Vol 548-549 ◽  
pp. 1196-1200
Author(s):  
Yong Mei Bao ◽  
Siqintana Bao
Keyword(s):  
Variable Coefficient ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Forced Term ◽  
Exact Soliton Solutions

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.

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.

Exact soliton solutions of the discrete modified Korteweg–de Vries (mKdV) equation

2010 ◽  
Vol 23 (2) ◽  
pp. 276-284 ◽  
Author(s):  
Yufeng Zhang ◽  
Jianqin Mei ◽  
Y. C. Hon
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
De Vries ◽  
Exact Soliton Solutions

Abundant Coherent Structures of the (2+1)-dimensional Broer-Kaup-Kupershmidt Equation

2001 ◽  
Vol 56 (9-10) ◽  
pp. 619-625 ◽  
Author(s):  
Jin-ping Ying ◽  
Sen-yue Lou
Keyword(s):  
Heat Conduction ◽  
Soliton Solution ◽  
Coherent Structures ◽  
Variable Coefficient ◽  
Heat Conduction Equation ◽  
Soliton Solutions ◽  
Conduction Equation ◽  
Painlevé Analysis ◽  
Straight Line ◽  
Exact Soliton Solutions

Abstract By using of the Bäcklund transformation, which is related to the standard truncated Painleve analysis, some types of significant exact soliton solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation are obtained. A special type of soliton solutions may be described by means of the variable coefficient heat conduction equation. Due to the entrance of infinitely many arbitrary functions in the general expressions of the soliton solution the solitons of the (2+1)- dimensional Broer-Kaup equation possess very abundant structures. By fixing the arbitrary functions appropriately, we may obtain some types of multiple straight line solitons, multiple curved line solitons, dromions, ring solitons and etc.

Bright and dark solitons for a generalized Korteweg-de Vries–modified Korteweg-de Vries equation with high-order nonlinear terms and time-dependent coefficients

2011 ◽  
Vol 89 (3) ◽  
pp. 253-259 ◽  
Author(s):  
Houria Triki ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Dark Soliton ◽  
Mkdv Equation ◽  
High Order ◽  
Time Dependent ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Envelope Solitons ◽  
De Vries ◽  
Exact Soliton Solutions

We consider a generalized Korteweg-de Vries–modified Korteweg-de Vries (KdV–mKdV) equation with high-order nonlinear terms and time-dependent coefficients. Bright and dark soliton solutions are obtained by means of the solitary wave ansatz method. The physical parameters in the soliton solutions are obtained as functions of the varying model coefficients. Parametric conditions for the existence of envelope solitons are given. In view of the analysis, we see that the method used is an efficient way to construct exact soliton solutions for such a generalized version of the KdV–mKdV equation with time-dependent coefficients and high-order nonlinear terms.

Multiple Soliton Solutions for a Variety of Coupled Modified Korteweg–de Vries Equations

2011 ◽  
Vol 66 (10-11) ◽  
pp. 625-631
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
De Vries ◽  
Coupled Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

We make use of Hirota’s bilinear method with computer symbolic computation to study a variety of coupled modified Korteweg-de Vries (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are obtained for each coupled equation. The resonance phenomenon of each coupled mKdV equation is proved not to exist.

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