Singular solitons in optical metamaterials by ansatz method and simplest equation approach

This paper derives singular 1-soliton solution for optical metamaterials. There are two integration approaches that obtains the solution. These are the ansatz approach and the simplest equation approach. The second method also leads to an additional set of solutions that emerge as a by-product. These are topological soliton, rational solution and singular periodic solution. The constraint conditions for the existence of these solutions are also exhibited. The numerical simulation of a topological 1-soliton solution is also exhibited.

[1]  Anjan Biswas,et al.  Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time-dependent coefficients by simplest equation approach , 2013 .

[2]  N. A. Kudryashov.  Simplest equation method to look for exact solutions of nonlinear differential equations , 2005 .

[3]  D. Christodoulides,et al.  Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler. , 2008, Optics express.

[4]  Anjan Biswas,et al.  New exact traveling wave solutions for DS-I and DS-II equations , 2012 .

[5]  Nikolay K. Vitanov,et al.  Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics , 2010 .

[6]  Nikolay K. Vitanov,et al.  Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs , 2011 .

[7]  Short Pulse Propagation in Wavelength Selective Index-Guided Photonic Crystal Fiber Coupler , 2008, IEEE Journal of Selected Topics in Quantum Electronics.

[8]  Anjan Biswas,et al.  Dispersive optical solitons with Schrödinger–Hirota equation , 2014 .

[9]  Nikolay K. Vitanov,et al.  Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity , 2010 .

[10]  D. Fan,et al.  Controllable Raman soliton self-frequency shift in nonlinear metamaterials , 2011 .

[11]  Nikolai A. Kudryashov,et al.  Exact solitary waves of the Fisher equation , 2005 .

[12]  Anjan Biswas,et al.  Optical Soliton Perturbation with Improved Nonlinear Schrödinger's Equation in Nano Fibers , 2013 .

[13]  N. Taghizadeh,et al.  The simplest equation method to study perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity , 2012 .

[14]  Holger Kantz,et al.  Modified method of simplest equation and its application to nonlinear PDEs , 2010, Appl. Math. Comput..

[15]  V. Veselago.  The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[16]  Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects , 2012, 1204.1623.

[17]  Anjan Biswas,et al.  Bright and dark solitons in optical metamaterials , 2014 .