0000000000731346

AUTHOR

U. Tanriver

showing 3 related works from this author

Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier

2015

Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…

Isochronous dynamicConservation lawApplied MathematicsMechanical EngineeringMathematical analysisAnharmonicityIsotonic potentialJacobi Last Multiplier (JLM)Simple harmonic motionInverse problemMultiplier (Fourier analysis)Nonlinear systemsymbols.namesakeSimple harmonic oscillatorMechanics of MaterialssymbolsNoether's theoremSettore MAT/07 - Fisica MatematicaLagrangianConservation lawsVariable (mathematics)MathematicsInternational Journal of Non-Linear Mechanics
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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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Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…

2016

In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…

Control and OptimizationComputational MechanicsDiscrete Mathematics and CombinatoricsStatistical and Nonlinear PhysicsExtended-Reduced Ostrovsky Equation Traveling Waves Singular Solutions Homoclinic and Heteroclinic Orbits Variational Solitary Waves
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