Related papers: Group classification of variable coefficient KdV-l…
Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears a crucial point for the exhaustive solution of the problem. We prove that all the…
A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new…
We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdV-mKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive group…
We carry out group analysis of a class of generalized fifth-order Korteweg-de Vries equations with time dependent coefficients. Admissible transformations, Lie symmetries and similarity reductions of equations from the class are classified…
Lie symmetries of K(m,n) equations with time-dependent coefficients are classified. Group classification is presented up to widest possible equivalence groups, the usual equivalence group of the whole class for the general case and…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form…
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…
Group classification of a class of Benjamin-Bona-Mahony (BBM) equations with time dependent coefficients is carried out. Two equivalent lists of equations possessing Lie symmetry extensions are presented: up to point equivalence within the…
In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are…
In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
We perform enhanced Lie symmetry analysis of generalized fifth-order Korteweg-de Vries equations with time-dependent coefficients. The corresponding similarity reductions are classified and some exact solutions are constructed.
We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of…
We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear…
We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method…
Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially…
Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove that this class is not normalized but can be presented as a…
We describe the equivalence groupoid of the class of general Burgers - Korteweg - de Vries equations with space-dependent coefficients. This class is shown to reduce by a family of equivalence transformations to a subclass whose usual…
In this work, the exact solutions for combined KdV-mKdV generalized equation as a linear superposition of Jacobi elliptic functions, $c_n(\xi,m)$, $d_n(\xi,m)$. When $m$ is set to one, the solution matches with well-known hyperbolic…