New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model

Abstract

The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

“…Several other methods including simple trigonometric ansatz methods [21,22], modified auxiliary equation technique [23,24], unified method [25,27], Jacobi elliptic function expansion method [28,29], Sine-Gordon expansion method [30,31], Exp (−ϕ(ξ ))-Expansion method [32,33], and modified simple equation method [34,35] are some other important and efficient methods to set exact solutions to nonlinear PDEs. For more details regarding models of nonlinear PDE and their solutions, one may refer to [36][37][38][39] and references therein. These methods In this article, we are concerned with implementing a new extended direct algebraic approach to derive a large family of exact solutions to both the KdV equation represented in Eq.…”

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

“…In this part, we use the improved Bernoulli sub-equation function method [24][25][26][27][28] for solutions eq. (1).…”

New Exact Solutions for the (3 + 1) Dimensional B-type Kadomtsev-Petviashvili Equation

“…In this part, we use the improved Bernoulli sub-equation function method (IBSEFM) (Baskonus and Bulut, 2015 a and b; Bulut et al2016;Dusunceli,2018Dusunceli, ,2019 for solutions eq. (1).…”