An exact solution for a derivative nonlinear Schrödinger equation
From MaRDI portal
Publication:4163830
DOI10.1063/1.523737zbMath0383.35015OpenAlexW2022028964MaRDI QIDQ4163830
Publication date: 1978
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.523737
Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Solutions to PDEs in closed form (35C05)
Related Items (only showing first 100 items - show all)
Conservation laws of some soliton equations with self-consistent sources ⋮ Conservation Laws, Hamiltonian Structure, Modulational Instability Properties and Solitary Wave Solutions for a Higher-Order Model Describing Nonlinear Internal Waves ⋮ Novel particular solutions, breathers, and rogue waves for an integrable nonlocal derivative nonlinear Schrödinger equation ⋮ Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques ⋮ Instability of degenerate solitons for nonlinear Schrödinger equations with derivative ⋮ On a new approach to generate spatial optical soliton in dielectric fibers ⋮ \(N\)-soliton solution of the Kundu-type equation via Riemann-Hilbert approach ⋮ Global well-posedness for the derivative nonlinear Schrödinger equation ⋮ The complex Hamiltonian system in the Gerdjikov-Ivanov equation and its applications ⋮ Statistical approach of modulational instability in the class of derivative nonlinear Schrödinger equations ⋮ Quasi-particle theory of Alfven soliton interaction in plasmas ⋮ Schemes for generating different nonlinear Schrödinger integrable equations and their some properties ⋮ Temporal solitons in nonlinear media modeled by modified complex Ginzburg Landau equation under collective variable approach ⋮ A generalized non-isospectral super AKNS hierarchy associated with the orthosymplectic Lie superalgebra \(osp(2, 2)\) ⋮ Binary Darboux transformation for the Gerdjikov-Ivanov equation ⋮ Generation of nonlinear modulated waves in a modified Noguchi electrical transmission network ⋮ On the origin of dual Lax pairs and their \(r\)-matrix structure ⋮ Inverse scattering transform for a nonlocal derivative nonlinear Schrödinger equation ⋮ A vector general nonlinear Schrödinger equation with \((m+n)\) components ⋮ Higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation: asymptotic analysis and emergence of rogue waves ⋮ \(M\)-truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ Fokas-Lenells equation: three types of Darboux transformation and multi-soliton solutions ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ New trace formulae for Sturm-Liouville operators on the Lasso-graph ⋮ A Riemann-Hilbert approach to a generalized nonlinear Schrödinger equation on the quarter plane ⋮ A new nonlinear wave equation: Darboux transformation and soliton solutions ⋮ Vector bright soliton interactions of the coupled Sasa-Satsuma equations in the birefringent or two-mode fiber ⋮ An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy ⋮ \(N\)-soliton solutions of the Fokas-Lenells equation for the plasma ion-cyclotron waves: inverse scattering transform approach ⋮ New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy ⋮ Higher-order mixed solution and breather solution on a periodic background for the Kundu equation ⋮ Two nonisospectral integrable hierarchies and its integrable coupling ⋮ Inverse scattering transform for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ Solitary waves with the Madelung fluid description: a generalized derivative nonlinear Schrödinger equation ⋮ Higher-order semirational solutions and nonlinear wave interactions for a derivative nonlinear Schrödinger equation ⋮ Painlevé-integrability and explicit solutions of the general two-coupled nonlinear Schrödinger system in the optical fiber communications ⋮ Modulation instability and dynamics for the Hermitian symmetric space derivative nonlinear Schrödinger equation ⋮ Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation ⋮ A \(\overline{\partial } \)-dressing method for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation ⋮ Riemann-Hilbert problem and \(N\)-soliton solutions for the \(n\)-component derivative nonlinear Schrödinger equations ⋮ Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case ⋮ Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities ⋮ Stable modes of derivative nonlinear Schrödinger equation with super-Gaussian and parabolic potential ⋮ Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras \(D_4^{(1)}\), \(D_4^{(2)}\), and \(D_4^{(3)}\) ⋮ Admissible boundary values for the Gerdjikov-Ivanov equation with asymptotically time-periodic boundary data ⋮ Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method ⋮ On the Riemann-Hilbert problem for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation ⋮ Spatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates ⋮ Gray optical dips of Kundu-Mukherjee-Naskar model ⋮ Dbar-dressing method for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ Breather, soliton and rogue wave of a two-component derivative nonlinear Schrödinger equation ⋮ Envelope solitary wave and periodic wave solutions in a Madelung fluid description of generalized derivative resonant nonlinear Schrödinger equation ⋮ Some localized wave solutions for the coupled Gerdjikov-Ivanov equation ⋮ A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems ⋮ Integration of the soliton hierarchy with self-consistent sources ⋮ Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation ⋮ Using a multi-component loop algebra to obtain an integrable extension of the KN hierarchy ⋮ A \((2 + 1)\)-dimensional multi-component AKNS integrable hierarchy and its expanding model ⋮ Derivative non-linear Schrödinger equation: singular manifold method and Lie symmetries ⋮ Gauge transform between the first order nonisospectral AKNS hierarchy and AKNS hierarchy ⋮ Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber ⋮ A Riemann-Hilbert approach to the multicomponent Kaup-Newell equation ⋮ Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov-Ivanov equation ⋮ Fractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy ⋮ Calculating adiabatic evolution of the perturbed DNLS/MNLS solitons ⋮ Bound and anti-bound soliton states for a quantum integrable derivative nonlinear Schrödinger model ⋮ Reduced Maxwell-Bloch equations with anisotropic dipole momentum ⋮ A multi-component matrix loop algebra and the multi-component Kaup-Newell (KN) hierarchy, as well as its integrable coupling system ⋮ Extended tanh-function method and reduction of nonlinear Schrödinger-type equations to a quadrature ⋮ An integrable \(\text{SO}(3,\mathbb{R})\)-counterpart of the Heisenberg soliton hierarchy ⋮ Darboux transformation and soliton-like solutions of nonlinear Schrödinger equations ⋮ A hierarchy of generalized AKNS equations, N-Hamiltonian structures and finite-dimensional involutive systems and integrable systems ⋮ A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations ⋮ Two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions ⋮ Asymptotic \(\Sigma\)-solutions of a singularly perturbed Benjamin-Bona-Mahony equation with variable coefficients ⋮ Demonstration of soliton solutions of DNLS equation by Liouville theorem ⋮ Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line ⋮ Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions ⋮ ADJOINT SYMMETRY CONSTRAINTS AND INTEGRABLE COUPLING SYSTEM OF MULTICOMPONENT KN EQUATIONS ⋮ Explicit quasi-periodic solutions of the Kaup-Newell hierarchy ⋮ Systematic construction of infinitely many conservation laws for certain nonlinear evolution equations in mathematical physics ⋮ Two integrable couplings of a generalized d-Kaup-Newell hierarchy and their Hamiltonian and bi-Hamiltonian structures ⋮ Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation ⋮ Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation ⋮ Rogue waves generation through multiphase solutions degeneration for the derivative nonlinear Schrödinger equation ⋮ The hierarchy of higher order solutions of the derivative nonlinear Schrödinger equation ⋮ A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws ⋮ Conservation laws and \(\tau\)-symmetry algebra of the Gerdjikov-Ivanov soliton hierarchy ⋮ Self-similar solutions to the derivative nonlinear Schrödinger equation ⋮ On a class of solutions to the generalized derivative Schrödinger equations ⋮ Invariant measures for the periodic derivative nonlinear Schrödinger equation ⋮ Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation ⋮ A \(\tau\)-symmetry algebra of the generalized derivative nonlinear Schrödinger soliton hierarchy with an arbitrary parameter ⋮ Two kinds of new integrable decompositions of the Gerdjikov-Ivanov equation ⋮ A tri-Hamiltonian formulation of a new soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\) ⋮ The rogue wave and breather solution of the Gerdjikov-Ivanov equation ⋮ Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation ⋮ New soliton hierarchies associated with the Lie algebra so(3,\(\mathbb{R}\)) and their Bi-Hamiltonian structures ⋮ Darboux transformation of the second-type derivative nonlinear Schrödinger equation
Cites Work
This page was built for publication: An exact solution for a derivative nonlinear Schrödinger equation
