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Bifurcation of Soliton Families from Linear Modes in Non‐ PT ‐Symmetric Complex Potentials
Author(s) -
Nixon Sean D.,
Yang Jianke
Publication year - 2016
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12117
Subject(s) - soliton , nonlinear system , bifurcation , perturbation (astronomy) , amplitude , constant (computer programming) , mathematics , motion (physics) , classical mechanics , physics , mathematical analysis , perturbation theory (quantum mechanics) , mathematical physics , quantum mechanics , computer science , programming language
Continuous families of solitons in the nonlinear Schrödinger equation with non‐ PT ‐symmetric complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special formg 2 ( x ) + i g ′ ( x ) , where g ( x ) is an arbitrary real function. Using this constant of motion, the second‐order complex soliton equation is reduced to a new second‐order real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous families of solitons bifurcate out from linear discrete modes in these non‐ PT ‐symmetric complex potentials. All analytical results are corroborated by numerical examples.