New general interaction solutions to the KPI equation via an optional decoupling condition approach

• Published in: Communications in nonlinear science & numerical simulation Vol. 103; p. 105939
• Main Authors: Lü, Xing, Chen, Si-Jia
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2021; Elsevier Science Ltd
• Subjects: An optional decoupling condition approach; Decoupling; Exact solutions; Lump sum; Lump-soliton solutions; Lump-stripe solutions; Nonlinear equations; Nonlinear evolution equations; Nonlinear systems; Partial differential equations; Schrodinger equation; Solitary waves; The KPI equation; The KPI equation; Lump-stripe solutions; 35A25; Lump-soliton solutions; An optional decoupling condition approach; 37K10
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2021.105939

•An optional decoupling condition approach is proposed for deriving the lump-stripe solutions and lump-soliton solutions to the KPI equation.•New and more general solutions are derived, and there exists a link between the two kinds of interaction solutions.•The optional decoupling condition approach can be applied to a wide range of nonlinear evolution equations. As a kind of analytical exact solutions to the nonlinear evolution equations, the interaction solutions are of great value in the study of the interacting mechanism in nonlinear science. In this paper, an optional decoupling condition approach is proposed for deriving the lump-stripe solutions and lump-soliton solutions to the KPI equation. We derive new and more general solutions to the KPI equation and discuss the link between the two kinds of interaction solutions, which has not been reported before. The interaction solutions to the KPI equation are analyzed and simulated numerically, which show that all the interaction phenomena are completely inelastic. Although we are concerned on the KPI equation in this paper, this approach can be applied to a wide class of nonlinear evolution equations and lays out the framework of deriving the lump-multi-stripe and/or lump-multi-soliton solutions.