Solitary waves for the MRLW equation

AbstractThis work presents a computational comparison study of quadratic, cubic, quartic and quintic splines for solving the modified regularized long wave (MRLW) equation. Collocation schemes with quadratic and cubic splines are found to be unconditionally stable. The fourth-order Runge–Kutta method has been used to solve the collocation schemes when quartic and quintic B-splines are used. The three invariants of motion have been evaluated to determine the conservation properties of the suggested algorithms. Comparisons of results due to different schemes with the exact values shows the accuracy and efficiency of the proposed schemes. Results corresponding to higher order splines are more accurate than those corresponding to lower order splines

New exact solutions of coupled generalized regularized long wave equations

In the present paper, we established a traveling wave solution by using sine-cosine functions algorithm and the Kudryashov Method for nonlinear partial differential equations. Different methods are used to obtain the exact solutions for different types of nonlinear partial differential equations such as, coupled generalized regularized long wave equation (CGRLW). We plot the exact solutions for these equations at different time levels. Keywords: Sine-cosine functions method, The Kudryashov method, Coupled GRLW

New solutions for the generalized q-deformed sinh-Gordon equation with q-calculus

Our objective in this paper is to investigate the sinh-Gordon equation’s generalization using a q-calculus. This equation explains systems with broken symmetries. The q-deformed sinh-Gordon equation adds noncommutativity and non-linearity, expanding on its original form. We compare two methods for solving this equation: RqDTM and VIM. RqDTM is a modified differential transform technique for q-deformed equations, whereas VIM utilizes an iterative approach. We give numerical results and compare the accuracy and efficiency of the solutions achieved using these approaches. This analysis evaluates the merits and disadvantages of each strategy for solving the q-deformed sinh-Gordon equation, offering insights into their applicability and performance