Soliton hierarchies and soliton solutions of type (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si1.svg"><mml:mrow><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e35" altimg="si2.svg"><mml:mrow><mml:mo>−</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:math> ) reduced nonlocal nonlinear Schrödinger equations of arbitrary even order
Wen‐Xiu Ma
Abstract
We present mixed-type reduced soliton hierarchies of nonlocal integrable nonlinear Schrödinger equations of arbitrary even order by conducting two nonlocal group reductions for the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on specific distributions of eigenvalues and adjoint eigenvalues, we construct soliton solutions by solving the corresponding reflectionless generalized Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues.
Topics & Concepts
Eigenvalues and eigenvectorsSolitonIntegrable systemType (biology)Order (exchange)Mathematical physicsMathematicsPhysicsNonlinear systemQuantum mechanicsEconomicsFinanceBiologyEcologyNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics