Nonlocal modified KdV equations and their soliton solutions by Hirota Method
Date
2019
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Source Title
Communications in Nonlinear Science and Numerical Simulation
Print ISSN
1007-5704
Electronic ISSN
Publisher
Elsevier
Volume
67
Issue
Pages
427 - 448
Language
English
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Abstract
We study the nonlocal modified Korteweg–de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz–Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then by using the Ablowitz–Musslimani reduction formulas, we find one-, two-, and three-soliton solutions of nonlocal mKdV and nonlocal complex mKdV equations. The soliton solutions of these equations are of two types. We give one-soliton solutions of both types and present only first type of two- and three-soliton solutions. We illustrate our solutions by plotting their graphs for particular values of the parameters.