Embedded Solitons and Conservation Law with χ^{(2)} and χ^{(3)} Nonlinear Susceptibilities |

M. Savescu
^{ a}, A.H. Kara^{ b}, S. Kumar^{ c}, E.V. Krishnan^{ d}, M. Zaka Ullah^{ e}, S.P. Moshokoa^{ f}, Qin Zhou^{ g} and A. Biswas^{e,f}^{a}Department of Mathematics, Kuztown University of Pennsylvania, 15200 Kutztown Road, Kuztown, PA-19530, USA
^{b}School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
^{c}Centre for Mathematics and Statistics, Central University of Punjab, Bathinda-151001, Punjab, India
^{d}Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al Khod 123, Muscat, Sultanate of Oman
^{e}Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box-80203, Jeddah-21589, Saudi Arabia
^{f}Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa
^{g}School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, PR China |

Received: October 27, 2016 |

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This paper studies embedded solitons that are confined to continuous spectrum, with χ^{(2)} and χ^{(3)} nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis. |

DOI: 10.12693/APhysPolA.131.297 PACS numbers/topics: solitons, χ ^{(2)} and χ^{(3)} nonlinearities, conservation laws |