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.
Highlights
Various complex nonlinear phenomena in different fields of nonlinear sciences such as fluid mechanic, plasma physics, and optical fibers can be expressed in the form of nonlinear partial differential equations (NPDEs)
Zayed et al [1] used the generalized Kudryashov in addressing some NPDEs arising in mathematical physics
Shang [4] obtained the exact solutions of the long-short wave resonance equation by using the extended hyperbolic function method
Summary
Various complex nonlinear phenomena in different fields of nonlinear sciences such as fluid mechanic, plasma physics, and optical fibers can be expressed in the form of nonlinear partial differential equations (NPDEs). Shang [4] obtained the exact solutions of the long-short wave resonance equation by using the extended hyperbolic function method. Wazzan [5] used the modified tanh-coth method in solving the generalized Burgers-fisher and Kuramoto-Sivashinsky equations. Various analytical approaches have been used in obtaining the exact solutions to the Konopelchenko-Dubrovsky equations. Sheng [27] used the improved F-expansion method in addressing (1), Wazwaz [28] employed the tanhsech method, the cosh-sinh method, and the exponential functions method for obtaining the analytical solutions to (1), and Kumar et al [29] solved the KD equations by traveling wave hypothesis and lie symmetry approach. Xia et al [33] employed the new modified extended tanh function method
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