The influence of initial solutions to exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations

TL;DR

This paper investigates how initial solutions affect the exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations, using bilinear forms and Hirota's method to derive soliton and wave solutions.

Contribution

It introduces a combined approach using bilinear forms and Hirota's method to find exact solutions of GNNVEs, demonstrating a generalized, computable technique for nonlinear PDEs.

Findings

Derived N-soliton solutions and three wave solutions for GNNVEs.

Showed the method's generalizability to other nonlinear PDEs.

Provided insights into the influence of initial solutions on exact solutions.

Abstract

The (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations (GNNVEs) are investigated in order to search the influence of initial solution to exact solutions. The GNNVEs are converted into the combined equations of differently two bilinear forms by means of the homogeneous balance of undetermined coefficients method. Accordingly, the two class of exact N-soliton solutions and three wave solutions are obtained respectively by using the Hirota direct method combined with the simplified version of Hereman and the three wave method. The proposed method is also a standard and computable method, which can be generalized to deal with some nonlinear partial differential equations (NLPDEs).