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Mathematics and Computers in Simulation, ISSN 0378-4754, 09/2016, Volume 127, pp. 131 - 150
► The theory of resonant solitons in Zakharov–Manakov system. ► Two different branches of solutions are found, arising from a bifurcation. ► The extended set... 
sl soliton solutions | Three wave interactions | Resonant solitons | Inverse scattering | Parametric interactions
Journal Article
Inverse Problems, ISSN 0266-5611, 10/2009, Volume 25, Issue 10, p. 105010
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 02/2012, Volume 85, Issue 2, p. 026604
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrodinger equations... 
STATES | PHYSICS, FLUIDS & PLASMAS | STABILITY | LIGHT | PHYSICS, MATHEMATICAL | BRIGHT SOLITONS | ARRAYS
Journal Article
Simulation, ISSN 0037-5497, 05/2005, Volume 81, Issue 5, pp. 339 - 352
A model of crowd motion that considers each pedestrian as a Newtonian particle subject to both physical and social forces was reported by Helbing, Farkas, and... 
social force models | multiagent simulations | Pedestrian dynamics | collective behavior | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | pedestrian dynamics
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 10/2010, Volume 43, Issue 43, p. 434019
Journal Article
Inverse Problems, ISSN 0266-5611, 05/2010, Volume 26, Issue 5, p. 055005
Journal Article
Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, 07/2012, Volume 45, Issue 14, pp. 145502 - 1-7
The resonant propagation of an optical pulse in a two-photon absorber with a coherent initial excitation of the medium may lead to a pulse steepening growing... 
LIGHT-PULSE | STIMULATED RAMAN-SCATTERING | OPTICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | Theorems | Flattening | Coherence | Atomic states | Derivatives | Excitation | Electric fields | Optical pulses
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2009, Volume 50, Issue 2, pp. 023504 - 023504-21
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation.... 
integral equations | PERTURBATION-THEORY | perturbation theory | INVERSE SCATTERING TRANSFORM | functional analysis | mathematical operators | PHYSICS, MATHEMATICAL | solitons | SELF-CONSISTENT SOURCES | eigenvalues and eigenfunctions | Physics - Exactly Solvable and Integrable Systems
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 2005, Volume 69, Issue 3, pp. 322 - 333
The interaction and propagation of optical pulses in a nonlinear waveguide array is described by the discrete nonlinear Schrödinger equation (1) i ∂ z ψ n = −... 
Discrete nonlinear Schrödinger equation | Variational solutions | Optical pulses | COMPUTER SCIENCE, SOFTWARE ENGINEERING | variational solutions | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | optical pulses | DYNAMICS | discrete nonlinear Schrodinger equation | SOLITON
Journal Article
Physical Review Letters, ISSN 0031-9007, 1999, Volume 83, Issue 10, pp. 1958 - 1961
We present a new type of soliton, found in models characterized by opposing dispersions and competing nonlinearities at fundamental and second harmonics. They... 
PHYSICS, MULTIDISCIPLINARY | STABILITY | NONLINEAR MEDIA
Journal Article
Physics of Plasmas, ISSN 1070-664X, 06/2004, Volume 11, Issue 6, pp. 3151 - 3164
The analytical modeling of the initialization stage of a relativistic magnetron of the A6 cylindrical design is presented, where only two dominant modes are... 
NEUTRAL ELECTRON FLOW | DENSITY PROFILES | STABILITY PROPERTIES | DIOCOTRON INSTABILITY | VACUUM DEVICE | PHYSICS, FLUIDS & PLASMAS | CROSSED-FIELD AMPLIFIER | PLANAR MAGNETRON | IN-CELL SIMULATION | DIODE | GEOMETRY
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 2009, Volume 159, Issue 3, pp. 806 - 818
We briefly review the Ablowitz-Kaup-Newell-Segur (AKNS) formalism for 1D+1D integrable systems starting with the Lax pair and continuing into integrable... 
Inverse scattering problem | Perturbation | Squared eigenfunction | Direct scattering problem | EVOLUTION | PHYSICS, MULTIDISCIPLINARY | squared eigenfunction | perturbation | inverse scattering problem | EQUATIONS | direct scattering problem | MODEL | PHYSICS, MATHEMATICAL | SCATTERING
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2001, Volume 152, pp. 340 - 354
It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton’s frequency (spatial or temporal)... 
Linear spectrum | Embedded solitons | Solitary waves | embedded solitons | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | NONLINEARITY | MODEL | PHYSICS, MATHEMATICAL | REVERSIBLE-SYSTEMS | WATER-WAVES | solitary waves | linear spectrum | MEDIA | HOMOCLINIC ORBITS | EQUATION | Physics - Pattern Formation and Solitons
Journal Article
Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 06/2020, Volume 85, p. 105244
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 06/2020, Volume 85
•Unstaggered-staggered soliton pairs observed in 1D and 2D DNLS.•Antisymmetric states in the form of discrete twisted solitons are observed in 1D.•Fundamental... 
Solitons | Unstaggered-staggered lattice | Variational approximation | Discrete nonlinear Schrödinger equations
Journal Article
Inverse Problems, ISSN 0266-5611, 04/2008, Volume 24, Issue 2, p. 025015
We study the AKNS (Ablowitz-Kaup-Newell-Segur) inverse scattering problem for rational reflection coefficients on a semi-infinite interval. We demonstrate that... 
MATHEMATICS, APPLIED | MATRIX FUNCTIONS | HALF-SOLITONS | BOUNDARY-VALUE PROBLEM | SHABAT EIGENVALUE PROBLEM | CANONICAL SYSTEMS | TRANSFORM | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | OPERATORS | FORMULAS
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2003, Volume 184, Issue 1, pp. 153 - 161
We develop the technique of the variational approximation (VA) for solitons in two directions. First, one may have a physical model which does not admit the... 
Variational approximation | Lagrangian | Second-harmonic-generation | Solitons | second-harmonic-generation | MATHEMATICS, APPLIED | WAVES | PHYSICS, MULTIDISCIPLINARY | NONLINEARITIES | variational approximation | PHYSICS, MATHEMATICAL | solitons
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 09/2016, Volume 127, p. 131
a* The theory of resonant solitons in Zakharov-Manakov system. a* Two different branches of solutions are found, arising from a bifurcation. a* The extended... 
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 08/2008, Volume 41, Issue 31, p. 315213
We consider several ways of how one could classify the various types of soliton solutions related to multicomponent nonlinear evolution equations which are... 
SYSTEM | REDUCTION PROBLEM | SPACE-TIME | MODELS | OPERATOR | PHYSICS, MULTIDISCIPLINARY | MEDIA | PHYSICS, MATHEMATICAL | RESONANT INTERACTION | SIMPLE LIE-ALGEBRAS | NERVE AXON EQUATIONS | SCATTERING
Journal Article
Physics of Plasmas, ISSN 1070-664X, 05/2006, Volume 13, Issue 5, pp. 053113 - 053113-13
Journal Article
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