Symbolic computation of bilinear equation for the KdV-type partial differential equations
Keywords:
Nonlinear Equation, Bilinearization, KdV equation, Boussinesq equation, CDG equation, SK equationAbstract
In this work, we focus on blinear equation, a crucial tool in study of nonlinear partial differential equations(NLPDEs).Using this technique, we also compare our results with already known methods like Hirota's technique.To convert a nonlinear partial differential equation (PDE) into bilinear form, the Hirota method is used.Numerous disciplines, including nonlinear dynamics, visual science, mathematical physics such as plasma physics, thermo-mechanics, optical science, and engineering sciences, employ the Hirota technique, a strong and precise mathematical tool, to find soliton solutions of nonlinear PDEs.These solitons can change depending on different values, which helps us to understand them better. We use a method called the Cole-Hopf transformation to make the equation easier to solve. In order to write a class of nonlinear PDEs in bilinear form, we offer a novel organized mathematical method. This approach is easy to utilize in programs like Mathematica and Maple because to its simplicity. The solutions are derived in simpler forms by performing transformations based on dependent variables and using tried-and-true mathematical techniques. These results show that the effectiveness of the computational algorithm.References
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