Related papers: Conservation Laws of Variable Coefficient Diffusio…
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously…
We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differential form and also their fractional counterparts. In Part 1,…
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publication aims to address this shortcoming. First, group…
This paper completes investigation of symmetry properties of nonlinear variable coefficient diffusion-convection equations of the form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. Potential symmetries of equations from the considered class are…
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are…
The group classification of variable coefficient quasilinear reaction-diffusion equations $u_t=u_{xx}+h(x)B(u)$ is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the…
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation…
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…
The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An…
A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to…
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…