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-expansion method (5) 5
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Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2008, Volume 13, Issue 3, pp. 584 - 592
Journal Article
Ain Shams Engineering Journal, ISSN 2090-4479, 12/2013, Volume 4, Issue 4, pp. 903 - 909
The modified simple equation (MSE) method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in engineering and... 
Tzitzeica–Dodd–Bullough equation | Nonlinear evolution equations | Modified KdV–Zakharov–Kuznetsov equation | Solitary wave solutions | Modified simple equation method | Exact solutions | Tzitzeica-Dodd-Bullough equation | Modified KdV-Zakharov-Kuznetsov equation
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 05/2018, Volume 15, Issue 5
We apply the Wick rotation to the Monge-Ampere equation of Tzitzeica graphs and we introduce the Wick-Tzitzeica solitons as complex functions solving the new... 
Tzitzeica equation | Wick rotation | Wick-Tzitzeica soliton | Monge-Ampère equation | Tzitzeica surface | Monge-Ampere equation | PHYSICS, MATHEMATICAL | SURFACES
Journal Article
Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 11/2017, Volume 149, pp. 439 - 446
In this paper, using the Painleve property, the traveling wave transformation, and the sine-Gordon expansion method (SGEM), the Tzitzéica type evolution... 
Sine-Gordon expansion method | Tzitzéica type equations | Nonlinear optics | Traveling wave solutions | Tzitzeica type equations | (G'/G)-EXPANSION METHOD | ZHIBER-SHABAT EQUATION | EVOLUTION-EQUATIONS | OPTICS | SOLITON
Journal Article
Zeitschrift für Naturforschung A, ISSN 0932-0784, 10/2018, Volume 73, Issue 10, pp. 883 - 892
We use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential... 
Tzitzéica | Weierstrass Function | 02.30.Ik | sine-Gordon | Dodd-Bullough | Liouville Equation | sinh-Gordon | 02.30.Hq | 04.20.Jb | Dodd-Bullough-Mikhailov | TRANSFORMATION | Tzitzeica | PHYSICS, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | DIFFERENTIAL-EQUATIONS | EVOLUTION | MODELS
Journal Article
Optik, ISSN 0030-4026, 02/2018, Volume 154, pp. 393 - 397
In this paper, we consider the Tzitzéica type equations and establish the travelling wave transformation which turns the nonlinear evolution equations into the... 
Tzitzéica type equations | Travelling wave transformation | Exponential rational function method | Exact solutions | Tzitzeica type equations | TRAVELING-WAVE SOLUTIONS | SOLITONS | DIFFERENTIAL-EQUATIONS | OPTICS
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 02/2014, Volume 34, Issue 2, pp. 557 - 566
We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzeica equation and prove global existence of small-norm solutions in... 
Conserved quantities | Global existence | Tzitzéica equation | Reduced Ostrovsky equation | Wave breaking | MATHEMATICS | Tzitzeica equation | MATHEMATICS, APPLIED | global existence | CAUCHY-PROBLEM | SHORT-PULSE | WELL-POSEDNESS | conserved quantities | SCATTERING | wave breaking | BACKLUND TRANSFORMATION
Journal Article
Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 11/2017, Volume 148, pp. 85 - 89
The Tzitzéica type equations arising in nonlinear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov, and Tzitzéica–Dodd–Bullough equations are solved... 
Novel exponential rational function method | Tzitzéica type equations | New exact solutions | Nonlinear optics | Tzitzeica type equations | SOLITON-SOLUTIONS | PERIODIC-WAVE | OPTICS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 8, pp. 2141 - 2167
Based on solutions of the stationary zero-curvature equation associated with a 3 x 3 matrix spectral problem, we introduce a trigonal curve related to the... 
MATHEMATICS | PERIODIC-SOLUTIONS | DARBOUX TRANSFORMATION | SYMMETRIES | SOLITONS | TRIGONAL CURVES | BOUSSINESQ | DECOMPOSITION | ABELIAN FUNCTIONS | TZITZEICA | Functions (mathematics) | Asymptotic properties | Mathematical analysis | Differentials | Meromorphic functions | Spectra | Representations
Journal Article
Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 08/2017, Volume 142, pp. 394 - 400
In this study, exact solutions of the nonlinear partial differential equations have been examined. The Tzitzeica-Dodd-Bullough, the nonlinear telegraph and the... 
Tzitzeica-Dodd-Bullough equation | Nonlinear telegraph equation | The trial equation method | Generalized Benjamin-Bona-Mahony equation | SOLITON-SOLUTIONS | OPTICS | Fluid dynamics | Differential equations
Journal Article
Balkan Journal of Geometry and its Applications, ISSN 1224-2780, 2014, Volume 19, Issue 2, pp. 11 - 22
We discuss the Tzitzeica equation and the spectral properties associated with its Lax operator L. We prove that the continuous spectrum of L is rotated with... 
Tzitzeica equation | Riemann-Hilbert problem | Resolvent of lax operator | MATHEMATICS | INVERSE SCATTERING | resolvent of Lax operator | Differential equations, Partial | Transformations (Mathematics) | Analysis
Journal Article
Journal of Geometry and Symmetry in Physics, ISSN 1312-5192, 2015, Volume 37, pp. 1 - 24
J. Geom. Symm. Phys. {\bf 37}, 1--24 (2015) We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end we use two methods... 
Hirota method | Zakharov-Shabat dressing method | Tzitzeica equations | singular soliton solutions | Physics - Exactly Solvable and Integrable Systems
Journal Article
应用数学学报:英文版, ISSN 0168-9673, 2016, Volume 32, Issue 2, pp. 461 - 468
In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough (TDB) equation. Since the double exp-function method has... 
74J35 | double exp-function method | Tzitzeica-Dodd-Bullough equation | 33F10 | solitary waves | one-soliton | Theoretical, Mathematical and Computational Physics | two-soliton | Mathematics | Applications of Mathematics | Math Applications in Computer Science | 35Q51
Journal Article
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