A generalization of the coupled integrable dispersionless equations

Abstract

The paper investigates an extension of the coupled integrable dispersionless equations, which describe the current‐fed string within an external magnetic field. By using the relation among the coupled integrable dispersionless equations, the sine‐Gordon equation and the two‐dimensional Toda lattice equation, we propose a generalized coupled integrable dispersionless system. N‐soliton solutions to the generalized system are presented in the Casorati determinant form with arbitrary parameters. By choosing real or complex parameters in the Casorati determinant, the properties of one‐soliton and two‐soliton solutions are investigated. It is shown that we can obtain solutions in soliton profile and breather profile. Copyright © 2016 John Wiley & Sons, Ltd.

CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System

“…e Darboux transformation of the CID system is studied based on a non-Abelian Lie group and expressed the matrix solutions in terms of quasideterminants [45]. e multisoliton solutions are constructed in terms of the Casorati determinants [46]. Based on the generalized Darboux transformation, the nth-order rogue wave solution of the CID equation is studied [47].…”

Darboux transformation and exact multisolitons for a matrix coupled dispersionless system

“…As we reduced the matrix CD system (1.1) into the usual CD system (1.2)-(1.3), sine-Gordon equation (1.4) and Maxwell-Bloch system (1.5), therefore, the matrix CD system can be regarded as a generalization of these equations. The Darboux/Bäcklund transformations for these equations have been studied in various references, such as [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The present work deals with the matrix CD system, DT and some exact solutions.…”

“…In the semi-classical limit the dispersion term of an ordinary integrable system is eliminated resulting in a dispersionless integrable system with no dispersion term. The coupled dispersionless (CD) integrable system is an important example of an integrable nonlinear dynamical system which has various applications in diverse areas, including theoretical physics, mathematics and engineering sciences [28][29][30][31][32][33].…”