Abstract
This paper deals with the analytical solutions for two models of special interest in mathematical physics, namely the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation and the (3+1)-dimensional generalized Boiti-Leon-Manna-Pempinelli equation. Using a modified version of the Fan sub-equation method, more new exact traveling wave solutions including triangular solutions, hyperbolic function solutions, Jacobi and Weierstrass elliptic function solutions have been obtained by taking full advantage of the extended solutions of the general elliptic equation, showing that the modified Fan sub-equation method is an effective and useful tool to search for analytical solutions of high-dimensional nonlinear partial differential equations.
Highlights
Nonlinear partial differential equations (NLPDEs) are important mathematical models to describe physical phenomena
The research on the explicit solution and integrability is helpful in clarifying the movement of the matter under nonlinear interaction and plays an important role in scientifically explaining the physical phenomena
It is interesting to note that research on solving fractional PDEs has attracted much attention recently, and there have been some new developments especially in solving time-fractional PDEs of the Fan sub-equations method (e.g., [25, 26])
Summary
Nonlinear partial differential equations (NLPDEs) are important mathematical models to describe physical phenomena. Solving the set of algebraic equations by using Maple, we can obtain many kinds of solutions depending on the special values chosen for hi
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