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Optics Letters, ISSN 0146-9592, 05/2010, Volume 35, Issue 9, pp. 1437 - 1439
We derive analytical 3D spatiotemporal similaritons and solitons of the generalized (3+1)-dimensional nonlinear Schrodinger equation with distributed... 
DISTRIBUTED COEFFICIENTS | WAVE | SOLITON-SOLUTIONS | OPTICS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2013, Volume 141, Issue 1, pp. 253 - 263
We present a new approach to studying a class of quasilinear problems including the so-called Modified Nonlinear Schrödinger Equations (MNLS). We show that... 
SCHRODINGER-EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 03/2015, Volume 56, Issue 3, p. 33508
We study the existence of positive solutions for a class of quasilinear elliptic equation. This model has been proposed in the self-channeling of a high-power... 
PHYSICS, MATHEMATICAL | SOLITON-SOLUTIONS
Journal Article
Optics Express, ISSN 1094-4087, 05/2016, Volume 24, Issue 9, pp. 10066 - 10077
We derive analytical solutions to the cubic-quintic nonlinear Schrodinger equation with potentials and nonlinearities depending on both propagation distance... 
LIGHT BULLETS | QUASI-SOLITON SOLUTIONS | OPTICS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 2015, Volume 56, Issue 7
In this work, we study the existence of multiple solutions to a class of quasilinear Schrodinger equation - Delta(p)u + V(x)vertical bar u vertical bar(p-2)u -... 
EXISTENCE | PHYSICS, MATHEMATICAL | SOLITON-SOLUTIONS
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 02/2012, Volume 85, Issue 2, p. 026601
The determinant representation of the n-fold Darboux transformation of the Hirota equation is given. Based on our analysis, the 1-soliton, 2-soliton, and... 
FIBERS | SOLITON-SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 01/2018, Volume 75, Issue 1, pp. 289 - 295
We aim to show the diversity of interaction solutions to the (2+1)-dimensional Ito equation, based on its Hirota bilinear form. The proof is given through... 
Lumps | Kinks | Hirota bilinear form | Solitons | MATHEMATICS, APPLIED | LUMP SOLUTIONS | KADOMTSEV-PETVIASHVILI EQUATION | WAVE | SOLITON-SOLUTIONS | SYMMETRY CONSTRAINT | SYSTEMS | NONLINEAR EVOLUTION-EQUATIONS | HIERARCHY
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 11/2017, Volume 58, Issue 11
We study the quasilinear Schrödinger equation arising from the nonlinear dynamics of the superfluid condensate − Δ u + λ u + κ 2 ( Δ u 2 ) u = β [ 1 α 3 − 1 (... 
SOLITON-SOLUTIONS | FILMS | PHYSICS, MATHEMATICAL | GROUND-STATES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 987 - 1008
In this paper, taking the Lax pairs of KdV equation as an illustrative example, with the help of a transformation of the spectral problem, another form of... 
Integrable system | Inversion | Action-angle coordinates | Soliton solutions
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2013, Volume 88, Issue 2, p. 023202
Exact explicit rogue wave solutions of the Sasa-Satsuma equation are obtained by use of a Darboux transformation. In addition to the double-peak structure and... 
FIBERS | SOLITON-SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | 3RD-ORDER DISPERSION | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 03/2013, Volume 87, Issue 3
Exact rogue wave solutions of the coupled Hirota equations are obtained by using a Darboux dressing transformation. An analysis of the spectral parameter... 
SCHRODINGER-EQUATIONS | SOLITON-SOLUTIONS | MODULATION INSTABILITY | PHYSICS, FLUIDS & PLASMAS | OPTICAL SOLITONS | PHYSICS, MATHEMATICAL | BRIGHT | WATER
Journal Article
Computers & Mathematics with Applications, ISSN 0898-1221, 09/2019
Journal Article
Physical Review A - Atomic, Molecular, and Optical Physics, ISSN 1050-2947, 01/2014, Volume 89, Issue 1
Analytical light-bullet solutions of a (3 + 1)-dimensional nonlinear Schrodinger equation with inhomogeneous diffraction or dispersion and nonlinearity in the... 
WAVES | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | LOCALIZED STRUCTURES | DISPERSION-DECREASING FIBER | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CRYSTALS | GENERATION | OPTICS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS | SIMILARITONS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 08/2012, Volume 218, Issue 24, pp. 11871 - 11879
The multiple exp-function algorithm, as a generalization of Hirota’s perturbation scheme, is used to construct multiple wave solutions to the (3 +... 
Hirota bilinear form | Multiple wave solution | Soliton equation | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | SOLITON-SOLUTIONS | FORM | NONLINEAR EVOLUTION-EQUATIONS | COMPLEXITON SOLUTIONS | TRANSFORMATIONS | Analysis | Algorithms
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 05/2019, Volume 60, Issue 5, p. 51501
In this paper, we consider the quasilinear Choquard equations  −ε2Δu+V(x)u−ε2uΔu2=εμ−N∫RN|u(y)|p|x−y|μdy|u(x)|p−2u(x)+|u|22*−2u,  where ε > 0 is a parameter, 0... 
SCHRODINGER-EQUATIONS | SOLITON-SOLUTIONS | GROUND-STATE SOLUTIONS | PHYSICS, MATHEMATICAL
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2014, Volume 89, Issue 1, p. 012907
We consider an extended nonlinear Schrodinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The... 
SOLITON-SOLUTIONS | PHYSICS, FLUIDS & PLASMAS | DISPERSION | MEDIA | OPTICAL-FIBERS | HEISENBERG SPIN CHAIN | PHYSICS, MATHEMATICAL | MODULATION | VORTEX
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2018, Volume 339, pp. 147 - 160
This paper obtains analytical solution of nonlinear Schrödinger equation in both time and space fractional terms. Two analytical approaches, Nucci's reduction... 
Nucci method | Nonlinear Schrödinger equation | Soliton solutions | Simplest equation method
Journal Article
by Li, QQ and Teng, KM and Wu, X
ADVANCES IN MATHEMATICAL PHYSICS, ISSN 1687-9120, 2018
We study the following generalized quasilinear Schrodinger equations with critical growth -div(g(2)(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2) +... 
SOLITON-SOLUTIONS | PLASMA | PHYSICS, MATHEMATICAL
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 08/2017, Volume 74, Issue 3, pp. 591 - 596
By using the Hirota bilinear form of the (2+1)-dimensional BKP equation, ten classes of interaction solutions between lumps and kinks are constructed through... 
Soliton | Lump | Bilinear form | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | BELL POLYNOMIALS | KDV-LIKE EQUATION | RESONANT SOLUTIONS | KADOMTSEV-PETVIASHVILI EQUATION | SOLITON-SOLUTIONS | BILINEAR EQUATIONS | SYMMETRY CONSTRAINT | TRIGONOMETRIC FUNCTION SOLUTIONS | KORTEWEG-DEVRIES
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2019, Volume 60, Issue 2
In this paper, we consider the following critical quasilinear problems in R-N : - Sigma(N)(i,j=1) D-j(b(ij)(v)D(i)v)+1/2 Sigma(N)(i,j=1)... 
SCHRODINGER-EQUATIONS | EXISTENCE | SOLITON-SOLUTIONS | PHYSICS, MATHEMATICAL | POSITIVE SOLUTIONS
Journal Article
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