Solutions of Initial Value Problems of Two (3+2)-Dimensional Integrable Nonlinear Equations via Non-local ${\bar{\partial }}$-Method

Abstract

The initial value problem (IVP) solutions of two (3+2)-dimensional integrable nonlinear equations, such as generalized Sawada-Kotera (SK) and generalized Date-Jimbo-Kashiwara-Miwa (DJKM) equations, which are constructed by the extension of the corresponding two-dimensional equations, are solved by means of the non-local ${\bar{\partial }}$-method. The above significant results provide a good inspiration for dealing with similar high-dimensional nonlinear equations.

Keywords

Sawada-Kotera (SK) equation / Date-Jimbo-Kashiwara-Miwa (DJKM) equation / Non-local ${\bar{\partial }}$-method / Initial value problem (IVP) / 35G2 / 45G10 / 45Q05

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Funding

National Natural Science Foundation of China(No.11971475)

Rights & permissions

Shanghai University