Author: Partha Guha

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AUTHOR

Partha Guha

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Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …

2014

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…

Equilibrium pointNumerical AnalysisNonlinear Sciences - Exactly Solvable and Integrable SystemsSeries (mathematics)Homoclinic and heteroclinic orbitApplied MathematicsMathematical analysisFOS: Physical sciencesMathematical Physics (math-ph)Phase planeTraveling waveNonlinear systemSPE and generalized SPE equationModeling and SimulationSaddle pointHomoclinic orbitExactly Solvable and Integrable Systems (nlin.SI)Singular solutionVariational solitary wavesSettore MAT/07 - Fisica MatematicaMathematical PhysicsConvergent seriesAnsatzMathematicsCommunications in Nonlinear Science and Numerical Simulation

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