Periodic and solitary wave solutions of some important physical models with variable coefficients. Issue 5 (3rd September 2021)

• Record Type: Journal Article
• Authors: Choi, Jin Hyuk; Kim, Hyunsoo; Sakthivel, R.
• Is Part Of: Waves in random and complex media. Volume 31:Issue 5(2021)
• Page Start: 891
• Page End: 910
• Publication Date: 2021-09-03
• Subjects: Integral and fractional order equations -- improved system method -- traveling wave solutions -- Painlevé test -- variable coefficients; Electromagnetic waves -- Periodicals; Electromagnetic waves -- Scattering -- Periodicals; 531.1133
• DOI: 10.1080/17455030.2019.1633029
• Languages: English
• ISSNs: 1745-5030

Abstract

ABSTRACT: In this paper, we construct the family of traveling wave solutions for various kinds of nonlinear integral and fractional order evolution equations with variable coefficients. Specifically, we consider the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and (1+1)-dimensional Benney-Luke equation as integeral order partial differential equations and the combined KdV-mKdV equation with time-dependent coefficients as fractional order partial differential equation. More precisely, the improved system technique has been implemented to obtain traveling wave solutions of the considered nonlinear evolution equations with variable coefficients. Further, the integrability of the combined fractional order KdV-mKdV equation with time-dependent coefficients is tested via Painlevé test. As a result, several exact traveling wave solutions have been successfully derived and subsequently their dynamical behaviors are visualized through graphically. The result reveals that the improved system technique is an effective and useful tool to obtain exact traveling wave solutions of both integral and fractional order nonlinear evolution equations with variable coefficients arising in various physical problems.