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. Biswase,f
aDepartment of Mathematics, Kuztown University of Pennsylvania, 15200 Kutztown Road, Kuztown, PA-19530, USA
bSchool of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
cCentre for Mathematics and Statistics, Central University of Punjab, Bathinda-151001, Punjab, India
dDepartment of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al Khod 123, Muscat, Sultanate of Oman
eOperator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box-80203, Jeddah-21589, Saudi Arabia
fDepartment of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa
gSchool 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