The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynami...The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other topics.In this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it.As a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic waves.To extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly.The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations.This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.展开更多
基金The authors thank to Faculty of Science,University of Rajshahi,Bangladesh for supporting project number(TURSP-2019/16).
文摘The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other topics.In this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it.As a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic waves.To extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly.The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations.This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.
