A direct method for finding similarity reductions of partial differential equations is applied to a specific case of the Grad–Shafranov equation. As an illustration of the method, the frequently used Solov’ev equilibrium is derived. The method is employed to obtain a new family of exact analytical solutions, which contain both the classical and nonclassical group-invariant solutions of the Grad–Shafranov equation and thus greatly extends the range of the available analytical solutions. All the group-invariant solutions based on the classical Lie symmetries are shown to be particular cases in the new family of solutions
Methods for transforming partial differential equations into forms more suitable for analysis and so...
We present a generalization of Lie\u27s method for finding the group invariant solutions to a system...
A nonlinear filtration equation in which the filter coefficient is an arbitrary function of the spec...
A direct method for finding similarity reductions of partial differential equations is applied to a ...
A direct method for finding similarity reductions of partial differential equations is applied to a ...
We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped tor...
AbstractIn this paper, based on classical Lie group method, with the help of Maple software, we stud...
textIn this paper, two equations from plasma physics are analyzed using two different mathematical ...
Problems of technological interest can very often be described by partial differential equations (PD...
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These...
We study the general applicability of the Clarkson–Kruskal’s direct method, which is known to be rel...
A variety of new exact solutions of partial di?erential equations and their systems have been found ...
When a partial differential equation in two independent variables is invariant to a group G of stret...
Includes bibliographical references (page 76)We have investigated a similarity analysis for a two-di...
Abstract. Approximate solutions of the Grad-Schlüter-Shafranov equation based on variational methods...
Methods for transforming partial differential equations into forms more suitable for analysis and so...
We present a generalization of Lie\u27s method for finding the group invariant solutions to a system...
A nonlinear filtration equation in which the filter coefficient is an arbitrary function of the spec...
A direct method for finding similarity reductions of partial differential equations is applied to a ...
A direct method for finding similarity reductions of partial differential equations is applied to a ...
We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped tor...
AbstractIn this paper, based on classical Lie group method, with the help of Maple software, we stud...
textIn this paper, two equations from plasma physics are analyzed using two different mathematical ...
Problems of technological interest can very often be described by partial differential equations (PD...
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These...
We study the general applicability of the Clarkson–Kruskal’s direct method, which is known to be rel...
A variety of new exact solutions of partial di?erential equations and their systems have been found ...
When a partial differential equation in two independent variables is invariant to a group G of stret...
Includes bibliographical references (page 76)We have investigated a similarity analysis for a two-di...
Abstract. Approximate solutions of the Grad-Schlüter-Shafranov equation based on variational methods...
Methods for transforming partial differential equations into forms more suitable for analysis and so...
We present a generalization of Lie\u27s method for finding the group invariant solutions to a system...
A nonlinear filtration equation in which the filter coefficient is an arbitrary function of the spec...