THERMAL SCIENCE
International Scientific Journal
MULTI-COMPLEXITON SOLUTIONS OF THE (2+1)-DIMENSIONAL ASYMMETRICAL NIZHNIK-NOVIKOV-VESELOV EQUATION
ABSTRACT
In this paper, the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation is investigated to acquire the complexiton solutions by the Hirota direct method. It is essential to transform the equation into Hirota bi-linear form and to build N-compilexiton solutions by pairs of conjugate wave variables.
KEYWORDS
PAPER SUBMITTED: 2020-03-01
PAPER REVISED: 2020-06-15
PAPER ACCEPTED: 2020-06-16
PUBLISHED ONLINE: 2021-03-27
THERMAL SCIENCE YEAR
2021, VOLUME
25, ISSUE
Issue 3, PAGES [2043 - 2049]
- Gao, X. Y., Bäcklund Transformation and Shock-Wave-Type Solutions for a Generalized (3+1)- Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation in Fluid Mechanics, Ocean Engineering, 96 (2015), Mar., pp. 245-247
- Gao, X. Y., Looking at a Non-Linear Inhomogeneous Optical Fiber through the Generalized Higher- Order Variable-Coefficient Hirota Equation, Applied Mathematics Letters, 73 (2017), Nov., pp. 143-149
- Du, Z., et al., Rogue Waves for the Coupled Variable-Coefficient Fourth-Order Non-Linear Schrodinger Equations in an Inhomogeneous Optical Fiber, Chaos, Solitons & Fractals, 109 (2018), Apr., pp. 90-98
- Zhao, X. H., et al., Multi-Soliton Interaction of a Generalized Schrödinger-Boussinesq System in a Magnetized Plasma, The European Physical Journal Plus, 132 (2017), 4, 192
- Liu, L., et al., Dark-Bright Solitons and Semirational Rogue Waves for the Coupled Sasa-Satsuma Equations, Physical Review E, 97 (2018), 5, ID 052217
- Yang, J. Y., et al., Lump and Lump-Soliton Solutions to the (2+1)-Dimensional Ito Equation, Analysis and Mathematical Physics, 8 (2018), 3, pp. 427-436
- Hirota, R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, Mass., USA, 2004
- Zhang, Y., Ma, W. X., Rational Solutions to a KdV-Like Equation, Applied Mathematics and Computation, 256 (2015), Apr., pp. 252-256
- Zhang, H. Q., Ma, W. X., Lump Solutions to the (2+1)-Dimensional Sawada-Kotera Equation, Nonlinear Dynamics, 87 (2017), 4, pp. 2305-2310
- Yuan, Y. Q., et al., Solitons for the (2+1)-Dimensional Konopelchenko-Dubrovsky Equations, Journal of Mathematical Analysis and Applications, 460 (2018), 1, pp. 476-486
- Wu, X. Y., et al., Rogue Waves for a Variable-Coefficient Kadomtsev-Petviashvili Equation in Fluid Mechanics, Computers & Mathematics with Applications, 76 (2018), 2, pp. 215-223
- Ma, W. X., Complexiton Solutions to the Korteweg-de Vries Equation, Physics Letters A, 301 (2002), 1, pp. 35-44
- Ma, W. X., Complexiton Solutions of the Korteweg-de Vries Equation with Self-Consistent Sources, Chaos, Solitons & Fractals, 26 (2005), 5, pp. 1453-1458
- An, H. L., Chen, Y., Numerical Complexiton Solutions for the Complex KdV Equation by the Homotopy Perturbation Method, Applied Mathematics and Computation, 203 (2008), 1, pp. 125-133
- Zhang, Y. Y., et al. New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations, Communications in Theoretical Physics, 46 (2006), 3, 407
- Ma, W. X., You, Y., Solving the Korteweg-de Vries Equation by Its Bi-linear Form: Wronskian Solutions, Transactions of the American mathematical society, 357 (2005), 5, pp. 1753-1778
- Zhou, Y., Ma, W X., Complexiton Solutions to Soliton Equations by the Hirota Method, Journal of Mathematical Physics, 58 (2017), 10, 101511
- Unsal, O., et al., Complexiton Solutions for Two Non-Linear Partial Differential Equations Via Modification of Simplified Hirota Method, Waves in Random and Complex Media, 27 (2017), 1, pp. 117-128
- Ma, W. X., Bi-linear Equations, Bell Polynomials and Linear Superposition Principle, Journal of Physics: Conference Series. IOP Publishing, 411 (2013), 1, 012021
- Wu, P. X., et al., Complexiton and Resonant Multiple Wave Solutions to the (2+1)-Dimensional Konopelchenko-Dubrovsky Equation, Computers & Mathematics with Applications, 76 (2018), 4, pp. 845-853
- Gao, L. N., et al., Resonant Behavior of Multiple Wave Solutions to a Hirota Bi-linear Equation, Computers & Mathematics with Applications, 72 (2016), 5, pp. 1225-1229
- Boiti, M., et al., On the Spectral Transform of a Korteweg-de Vries Equation in Two Spatial Dimensions, Inverse problems, 2 (1986), 3, 271
- Hu, H. C., et al., Variable Separation Solutions Obtained from Darboux Transformations for the Asymmetric Nizhnik-Novikov-Veselov System, Chaos, Solitons & Fractals, 22 (2004), 2, pp. 327-334
- Yong, C., Qi, W., A Series of New Double Periodic Solutions to a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equation, Chinese Physics, 13 (2004), 11, 1796
- Dai, C. Q., Zhou, G. Q., Exotic Interactions Between Solitons of the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System, Chinese Physics, 16 (2007), 5, 1201
- Fan, E., Quasi-Periodic Waves and an Asymptotic Property for the Asymmetrical Nizhnik-Novikov-Veselov Equation, Journal of Physics A: Mathematical and Theoretical, 42 (2009), 9, 095206
- Zhao, Z., et al. Lump Soliton, Mixed Lump Stripe and Periodic Lump Solutions of a (2+1)-Dimensional Asymmetrical Nizhnik-Novikov-Veselov Equation, Modern Physics Letters B, 31 (2017), 14, ID 1750157
- He, J. H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
- Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
- Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Hairs (vol. 26, 1850086, 2018), Fractals, 27 (2019), 5, ID 1992001
- Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Hairs (vol. 26, 1850086, 2018), Fractals, 26 (2018), 6, ID 1850086
- Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448
- He, J. H., A Short Review on Analytical Methods for to a Fully Fourth-Order Non-Linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, 30 (2020), 11, pp. 4933-4943
- Shen, Y., He, J. H., Variational Principle for a Generalized KdV Equation in a Fractal Space, Fractals, 28 (2020), 4, ID 2050069
- Li, X. J., et al., A Fractal Two-Phase Flow Model for the Fiber Motion in a Polymer Filling Process, Fractals, 28 (2020), 5, ID 2050093