期刊
STUDIES IN APPLIED MATHEMATICS
卷 136, 期 4, 页码 459-483出版社
WILEY-BLACKWELL
DOI: 10.1111/sapm.12117
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资金
- Air Force Office of Scientific Research [USAF 9550-12-1-0244]
- National Science Foundation [DMS-1311730]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1311730] Funding Source: National Science Foundation
Continuous families of solitons in the nonlinear Schrodinger 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 form g2(x)+ig(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.
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