Lie symmetries, solitary wave solutions, and conservation laws of coupled KdV-mKdV equation for internal gravity waves

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Soliton solutions (35C08) Symmetries, invariants, etc. in context of PDEs (35B06)

Cites Work

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Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation
On traveling wave solutions to combined KdV-mKdV equation and modified Burgers-KdV equation
A new conservation theorem
Solitary wave solutions for a generalized KdV-mKdV equation with variable coefficients
Similarity methods for differential equations
Analytical and numerical solution of a coupled KdV-MKdV system
Lie symmetry analysis and conservation law of variable-coefficient Davey-Stewartson equation
Lie symmetry, nonlocal symmetry analysis, and interaction of solutions of a \((2+1)\)-dimensional KdV-mKdV equation
On Lie symmetries and soliton solutions of \((2+1)\)-dimensional Bogoyavlenskii equations
A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations
Integrating factors, adjoint equations and Lagrangians
A numerical application of the decomposition method for the combined KdV-MKdV equation
On the symmetry analysis and conservation laws of the (1 + 1)-dimensional Hénon-Lane-Emden system
Nonlinear self-adjointness and conservation laws
Codimension two Lie invariant solutions of the modified Khokhlov–Zabolotskaya–Kuznetsov equation
Lie symmetry analysis for complex soliton solutions of coupled complex short pulse equation
Lie symmetry analysis, symmetry reductions with exact solutions, and conservation laws of (2+1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order in plasma physics
Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equation
Lie symmetries and conservation laws of the Fokker‐Planck equation with power diffusion
On the exact solutions, lie symmetry analysis, and conservation laws of Schamel–Korteweg–de Vries equation
Exact solutions to the combined KdV–mKdV equation by the extended mapping method
Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws
Symmetries and differential equations
Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation
Lie group of invariance technique for analyzing propagation of strong shock wave in a rotating non‐ideal gas with azimuthal magnetic field

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