Approximate symmetries and similarity solutions for wave equations on liquid films

PDEs in connection with fluid mechanics (35Q35) Thin fluid films (76A20) Applications of Lie groups to the sciences; explicit representations (22E70) Lie algebras of Lie groups (22E60)

Cites Work

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On the linearization of second-order ordinary differential equations to the Laguerre form via generalized Sundman transformations
A numerical comparison of a Kawahara equation
Comparison of approximate symmetry methods for differential equations
A note on the stability for Kawahara-KdV type equations
On the Benney-Lin and Kawahara equations
\(n^{\text{th}}\)-order approximate Lagrangians induced by perturbative geometries
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Two-dimensional solitary waves for a Benney-Luke equation
Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems
Symmetry reduction, exact group-invariant solutions and conservation laws of the Benjamin-Bona-Mahoney equation
Approximate Noether symmetries
New multipliers of the barotropic vorticity equations
Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations
Nonlocal symmetries, exact solutions and conservation laws of the coupled Hirota equations
Symmetry, Singularities and Integrability in Complex Dynamics III: Approximate Symmetries and Invariants
Approximate Equations for Long Nonlinear Waves on a Viscous Fluid
Nonlinear ordinary differential equations: A discussion on symmetries and singularities
Lie symmetries of a coupled nonlinear Burgers-heat equation system
On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter
Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation
Conservation of Hamiltonian using Continuous Galerkin Petrov time discretization scheme
Conservation laws for a Boussinesq equation.
APPROXIMATE SYMMETRIES
Finite amplitude side-band stability of a viscous film
Lie Algebras of Approximate Symmetries
A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals
On the Interactions of Permanent Waves of Finite Amplitude
Approximate symmetries of Hamiltonians
Long Waves on Liquid Films