Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 67, Issue -, Pages 427-448Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2018.07.013
Keywords
Ablowitz-Musslimani reduction; Nonlocal mKdV equations; Hirota bilinear form; Soliton solutions
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Funding
- Scientific and Technological Research Council of Turkey (TUBITAK)
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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. (C) 2018 Elsevier B.V. All rights reserved.
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