Novel multiple soliton solutions for some nonlinear PDEs via multiple method

In this work, the analytic solutions for different types of nonlinear partial differential equations are obtained using the multiple Exp-function method. We consider the stated method for the (3+1)-dimensional generalized shallow water-like (SWL) equation, the (3+1)-dimensional Boiti-Leon- Manna-Pempinelli (BLMP) equation, (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili (VC B-type KP) equation and the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. We obtain multi classes of solutions containing one-soliton, two-soliton, and triple-soliton solutions. All the computations have been performed using the software package Maple. The obtained solutions include three classes of soliton wave solutions in terms of one-wave, two-waves, and three-waves solutions. Then the multiple soliton solutions are presented with more arbitrary autocephalous parameters, in which the one, two, and triple solutions localized in all directions in space. Moreover, the obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. The different types of obtained solutions of aforementioned nonlinear equations arising in fluid dynamics and nonlinear phenomena.

Automated summary

In this work, analytic solutions for various types of nonlinear partial differential equations are obtained using the multiple Exp-function method. The solutions include multiple classes of soliton solutions and have been computed using the software package Maple. The obtained solutions exhibit the effects of nonlinearity and are applicable in fluid dynamics and other nonlinear phenomena.