A systematic construction of parity-time ($\mathcal{PT}$ )-symmetric and non-$\mathcal{PT}$ -symmetric complex potentials from the solutions of various real nonlinear evolution equations

DOI10.1088/1751-8121/aa853dzbMath1380.37124arXiv1708.03083OpenAlexW2743923685MaRDI QIDQ4591266

Avinash Khare, K. Tamilselvan, T. Kanna

Publication date: 14 November 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03083

zbMATH Keywords

solitonparity-time symmetryWadati potential

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) PDEs in connection with quantum mechanics (35Q40) Soliton solutions (35C08)

Related Items

General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system, Complex symmetric evolution equations

Cites Work

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• Partial differential equations and solitary waves theory
• On the propagation of nonlinear solitary waves in a distributed Schottky barrier diode transmission line
• Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
• The sine-Gordon model and its applications. From pendula and Josephson junctions to gravity and high-energy physics
• The Modified Korteweg-de Vries Equation
• Wave Propagation in Nonlinear Lattice. II
• Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Exactly Solvable Wadati Potentials in the PT-Symmetric Gross-Pitaevskii Equation
• On some classes of mKdV periodic solutions
• Generation of solitons and breathers in the extended Korteweg–de Vries equation with positive cubic nonlinearity
• Superposition of elliptic functions as solutions for a large number of nonlinear equations
• Breather solutions and breather lattice solutions to the sine-Gordon equation