Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I symmetry preserving and symmetry breaking solutions

In this paper, we construct degenerate soliton solutions (which preserve PT -symmetry/break PT -symmetry) to the nonlocal Manakov system through a nonstandard bilinear procedure. Here, by degenerate we mean the solitons that are present in both the modes which propagate with same velocity. The degen...

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Bibliographic Details
Published inNonlinear dynamics Vol. 95; no. 1; pp. 343 - 360
Main Authors Stalin, S., Senthilvelan, M., Lakshmanan, M.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2019
Springer Nature B.V
Subjects
Automotive Engineering
Broken symmetry
Classical Mechanics
Control
Curvature
Dynamical Systems
Eigenvalues
Engineering
Mechanical Engineering
Original Paper
Solitary waves
Symmetry
Vibration
Hirota’s bilinear method
Nonlocal Manakov equation
Soliton solutions
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Summary:In this paper, we construct degenerate soliton solutions (which preserve PT -symmetry/break PT -symmetry) to the nonlocal Manakov system through a nonstandard bilinear procedure. Here, by degenerate we mean the solitons that are present in both the modes which propagate with same velocity. The degenerate nonlocal soliton solution is constructed after briefly indicating the form of nondegenerate one-soliton solution. To derive these soliton solutions, we simultaneously solve the nonlocal Manakov equation and a pair of coupled equations that arise from the zero curvature condition. The latter consideration yields general soliton solution which agrees with the solutions that are already reported in the literature under certain specific parametric choice. We also discuss the salient features associated with the obtained degenerate soliton solutions.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4567-5