Symmetry solutions and conserved vectors for a generalized short pulse equation. (English) Zbl 1490.35019
Summary: This work investigates a generalized short pulse equation. The short pulse equation governs the generation of ultra short optical pulses in nonlinear media. Firstly, we find its Lie symmetries and later utilize them to secure an optimal system of one-dimensional subalgebras (OSOSs). Thereafter, invariant solutions are determined under each element of the OSOSs. Three different cases for the constants \(a\) and \(b\) in the equation are discussed, viz., \(a\) and \(b\) not zero simultaneously; \(a=0\) but \(b\neq 0\); \(a\neq 0\) but \(b=0\). We also depict graphically the 3D and 2D representations of some of the gained solutions for the underlying equation. Secondly, by invoking the general multiplier method we acquire conserved vectors for the generalized short pulse equation.
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35C05 | Solutions to PDEs in closed form |
| 35L65 | Hyperbolic conservation laws |
Keywords:
generalized short pulse equation; Lie symmetries; exact solutions; conserved vectors; general multiplier method; optimal system of one-dimensional subalgebrasSoftware:
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