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Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 4, pp. 950 - 959
A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N... 
Hirota’s bilinear form | [formula omitted]-wave solution | Soliton equations | Hirota's bilinear form | N-wave solution | COMMUTATIVITY | MATHEMATICS, APPLIED | BACKLUND-TRANSFORMATIONS | HIERARCHY | Traveling waves | Construction specifications | Mathematical models | Algorithms | Mathematical analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2014, Volume 248, pp. 456 - 462
In this paper, Bell-polynomial method is used to study the integrability of a (3+1)-dimensional nonlinear evolution equation. We get the bilinear... 
(3 + 1)-dimensional nonlinear evolution equation | Binary Bell polynomial | N-wave solution | Bäcklund transformation | Periodic solitary wave solution | MATHEMATICS, APPLIED | BILINEAR EQUATIONS | Backlund transformation | (3+1)-dimensional nonlinear evolution equation
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 1/2017, Volume 190, Issue 1, pp. 43 - 51
We propose a linearizable version of a multidimensional system of n-wave-type nonlinear partial differential equations (PDEs). We derive this system using the... 
periodic solution | n -wave equation | Theoretical, Mathematical and Computational Physics | dressing method | linearizable equation | Applications of Mathematics | Physics | n-wave equation | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Differential equations | Physics - Exactly Solvable and Integrable Systems
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2016, Volume 71, Issue 6, pp. 1242 - 1247
Linear subspaces of hyperbolic and trigonometric function solutions to generalized bilinear equations are analyzed. Necessary and sufficient conditions are... 
[formula omitted]-wave solution | Linear superposition principle | Generalized bilinear equations | N-wave solution | MATHEMATICS, APPLIED | SUBSPACES | WAVE SOLUTIONS | COMPLEXITON SOLUTIONS | Concretes | Mathematical models | Algorithms | Trigonometric functions | Subspaces | Mathematical analysis
Journal Article
Pure and Applied Geophysics, ISSN 0033-4553, 8/2017, Volume 174, Issue 8, pp. 3209 - 3218
Journal Article
International Journal of Nonlinear Sciences and Numerical Simulation, ISSN 1565-1339, 07/2017, Volume 18, Issue 5, pp. 395 - 401
Journal Article
Communications on Pure and Applied Analysis, ISSN 1534-0392, 01/2017, Volume 16, Issue 1, pp. 253 - 272
This paper is focused on the study of the large time asymptotic for solutions to the viscous Burgers equation and also to the adhesion model via heat equation.... 
Schwartz class | Cole-Hopf transformation | N-wave solutions | Heat equation | Truncated moment problem | MATHEMATICS | MATHEMATICS, APPLIED | heat equation | CONVERGENCE | truncated moment problem | MOMENTS
Journal Article
Romanian Reports of Physics, ISSN 1221-146X, 2013, Volume 58, Issue 5-6
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 06/2000, Volume 41, Issue 6, pp. 4188 - 4237
A new method for studying boundary value problems for linear and for integrable nonlinear partial differential equations (PDE’s) in two dimensions is reviewed.... 
DAVEY-STEWARTSON | N-WAVE | INVERSE SCATTERING TRANSFORM | FUNDAMENTAL PRINCIPLE | BOUNDARY-VALUE-PROBLEM | SYSTEMS | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | EXPLICIT VERSION | DEPENDENT SCHRODINGER-EQUATION
Journal Article
Journal of Hydraulic Research, ISSN 0022-1686, 01/2020, Volume 58, Issue 1, pp. 47 - 59
Using the recently developed bottom-tilting wave maker, run-ups of very long waves are investigated on an adjustable plane beach. Both leading-elevation waves... 
surf-similarity parameter | tsunami | Long waves | run-up | wave breaking | BREAKING | ENGINEERING, CIVIL | N-WAVES | TSUNAMI RUNUP | WATER RESOURCES | SURF-SIMILARITY | Shallow water equations | Slopes | Surf | Elevation | Nonlinear equations | Parameters | Similarity | Waves | Solitary waves | Shallow water | Equations
Journal Article
Nonlinearity, ISSN 0951-7715, 07/2012, Volume 25, Issue 7, pp. 1967 - 1979
We introduce a nonlinear 2 + 1 dimensional system of equations related to the first-order nonstrict hyperbolic system. On the basis of the analysis of... 
MATHEMATICS, APPLIED | MULTIDIMENSIONAL SOLITONS | N-WAVE | NON-LINEAR EQUATIONS | PHYSICS, MATHEMATICAL | PLANE | Nonlinear equations | Inverse scattering | Integral equations | Mathematical analysis | Exact solutions | Nonlinear evolution equations | Nonlinearity | Hyperbolic systems
Journal Article
by Qu, K and Ren, X.Y and Kraatz, S
Applied Ocean Research, ISSN 0141-1187, 02/2017, Volume 63, pp. 36 - 48
•An numerical wave model was presented to reproduce the solitary wave and the depression leading tsunami-like wave based on the incompressible two phase flow... 
Solitary wave | N-wave | Navier-stokes equations | Wave run-up | Breakwater | Volume of fluid | RUN-UP | EQUATIONS | SIMULATION | FLOW | ENGINEERING, OCEAN | OCEANOGRAPHY | GENERATION | Volume fluid | Wave propagation | Numerical analysis | Seismology | Analysis | Investigations
Journal Article
COMMUNICATIONS IN THEORETICAL PHYSICS, ISSN 0253-6102, 01/2020, Volume 72, Issue 1, p. 15004
We generalize the partial derivative-dressing method to investigate a (2 + 1)-dimensional lattice, which can be regarded as a forced (2 + 1)-dimensional... 
TRANSFORMATION | explicit solution | INVERSE SCATTERING | EVOLUTION | N-WAVE | PHYSICS, MULTIDISCIPLINARY | discrete (2+1)-dimensional three-wave equation | partial derivative-dressing method | SYSTEMS
Journal Article
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 2008, Volume 1022, pp. 17 - 29
Inspired by the simpler, exact analysis of Burgers equation, we give exact or asymptotic solutions of a class of generalized Burgers equations, subject to... 
N-waves | Nonlinear equations | Model equations
Conference Proceeding
Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 7, pp. 3925 - 3933
In this paper, we study the polynomials possessing the linear superposition principle (LSP) and dispersion relation. A necessary and sufficient condition is... 
Hirota bilinear equations | N-wave solution | Linear superposition principle | Dispersion relation | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | DE-VRIES EQUATION | Construction | Mathematical models | Dispersions | Computation | Mathematical analysis
Journal Article
Journal of Hydraulic Research, ISSN 0022-1686, 07/2017, Volume 55, Issue 4, pp. 557 - 572
Journal Article
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