Search results for "SPE and generalized SPE equation"

showing 2 items of 2 documents

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
researchProduct

Corrigendum to “Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infi…

2022

Section 7 of the original paper contained several errors which are corrected here. Equations (54) and (55) are incorrect. In the following, the corrected versions of these equations are given and the subsequent results of Section 7 are also revised.

Traveling waveNumerical AnalysisHomoclinic and heteroclinic orbitSPE and generalized SPE equationApplied MathematicsModeling and SimulationSingular solutionVariational solitary wavesSettore MAT/07 - Fisica MatematicaCommunications in Nonlinear Science and Numerical Simulation
researchProduct