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The degenerate coupled multi-Korteweg–de Vries equations for coupled multiplicity $$l=3$$ l=3 are studied. The equations, also known as three-field Kaup–Boussinesq equations, are considered for invariant analysis and conservation laws. The classical Lie’s symmetry method is used to analyse the symmetries of equations. Based on the Killing’s form, which is invariant of adjoint action, the full classification...
In this paper, we apply three different techniques, namely, the sine–cosine method, the new extended auxiliary equation method and the modified simple equation method for constructing many new exact solutions with parameters as well as bright–dark, singular and other soliton solutions of the coupled nonlinear Schrödinger equations. The solutions of these coupled nonlinear equations are compared with...
Casson fluid flow has numerous functional applications in food processing, metallurgy, drilling and bio-engineering operations. The significance of Casson fluid in cylindrical coordinates has recently attracted researchers because of the numerical and experimental analyses of the fluid. Due to the lack of fractional analytical approaches, this paper is trying to examine the magnetic effect and thermal...
This paper investigates the new coupled $$(2+1)$$ (2+1) -dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method. Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons...
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