Transformation and integrability of a generalized short pulse equation
Copyright policy )Transformation and integrability of a generalized short pulse equation
By means of transformations to nonlinear Klein-Gordon equations, we show that a generalized short pulse equation is integrable in two (and, most probably, only two) distinct cases of its coefficients. The first case is the original short pulse equation (SPE). The second case, which we call the single-cycle pulse equation (SCPE), is a previously overlooked scalar reduction of a known integrable system of coupled SPEs. We get the Lax pair and bi-Hamiltonian structure for the SCPE and show that the smooth envelope soliton of the SCPE can be as short as only one cycle of its carrier frequency.
13 pages, 4 figures
Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), Pattern Formation and Solitons (nlin.PS), Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Nonlinear Sciences - Pattern Formation and Solitons, integrable systems, single-cycle pulse, Soliton solutions, solitons, Exactly Solvable and Integrable Systems (nlin.SI), short pulse equation, Mathematical Physics, Second-order nonlinear hyperbolic equations
Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), Pattern Formation and Solitons (nlin.PS), Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Nonlinear Sciences - Pattern Formation and Solitons, integrable systems, single-cycle pulse, Soliton solutions, solitons, Exactly Solvable and Integrable Systems (nlin.SI), short pulse equation, Mathematical Physics, Second-order nonlinear hyperbolic equations
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