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- W2020346719 abstract "In this paper we present a method of constructing explicit classes of solutions of the Chaplygin and Born–Infeld systems of equations in 1+1 dimensions. The approach adopted here is based on the symmetry reduction method for PDE’s. A systematic use of the subgroup structure of the invariance group is made to generate symmetry variables. We concentrate only on the case when the symmetry variables are invariants of the subgroups having dimension one. The set of symmetry variables enables us to reduce, after some transformation, the original equations to many possible ODE’s. We describe in detail how a composition of Lie subalgebras and singularity analysis applied to these systems provides us with classes of analytic solutions. Several new types of algebraic, rational and solitonlike solutions (among them kinks, bumps and multiple wave solutions) have been obtained in explicit form. We discuss also the existence of several classes of separable solutions admitted by the Chaplygin and Born–Infeld equations. Some physical interpretation of these results in the areas of fluid dynamics and field theory are given." @default.
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- W2020346719 date "2003-06-19" @default.
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- W2020346719 title "Group-invariant solutions of relativistic and nonrelativistic models in field theory" @default.
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- W2020346719 doi "https://doi.org/10.1063/1.1576496" @default.
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