December  2015, 8(6): 1155-1164. doi: 10.3934/dcdss.2015.8.1155

Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation

1. 

Computer Engineering Technique Department Al-Rafidain, University College, Baghdad, Iraq

2. 

Department of Engineering Sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran

3. 

Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, United States

Received  May 2015 Revised  August 2015 Published  December 2015

This paper obtains soliton and other solutions to the Gardner-Kadomtsev-Petviashvili equation that models shallow water wave equation in (1+2)-dimensions. There are three types of integration architectures that will be employed in order to obtain several forms of solution to this model. These are traveling wave hypothesis, improved $G^{\prime}/G$-expansion method and finally the tanh-coth hypothesis. The constraint conditions that are needed, for these solutions to exist, are also reported.
Citation: Anwar Ja'afar Mohamad Jawad, Mohammad Mirzazadeh, Anjan Biswas. Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1155-1164. doi: 10.3934/dcdss.2015.8.1155
References:
[1]

Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 734-748. doi: 10.1016/j.cnsns.2007.12.004.  Google Scholar

[2]

Romanian Journal of Physics, 58 (2013), 729-748.  Google Scholar

[3]

Advanced Studies in Theoretical Physics, 2 (2008), 787-794.  Google Scholar

[4]

Applied Mathematics and Computation, 214 (2009), 645-647. doi: 10.1016/j.amc.2009.04.001.  Google Scholar

[5]

Applied Mathematics and Computation, 217 (2010), 1771-1773. doi: 10.1016/j.amc.2009.09.042.  Google Scholar

[6]

Journal of Applied Fluid Mechanics, 7 (2014), 603-609. Google Scholar

[7]

Romaninan Reports in Physics, 65 (2013), 27-62. Google Scholar

[8]

Journal of Modern Optics, 60 (2013), 1627-1636. doi: 10.1080/09500340.2013.850777.  Google Scholar

[9]

European Physical Journal, Plus, 128 (2013), p140. Google Scholar

[10]

Nonlinear Dynamics, 66 (2011), 497-507. doi: 10.1007/s11071-010-9928-7.  Google Scholar

[11]

Journal of Applied Fluid Mechanics, 6 (2013), 339-350. Google Scholar

[12]

Journal of Applied Fluid Mechanics, 7 (2014), 711-718. Google Scholar

[13]

Computational and Applied Mathematics, 33 (2014), 831-839. doi: 10.1007/s40314-013-0098-3.  Google Scholar

[14]

Pramana, 81 (2013), 225-236. Google Scholar

[15]

Pramana, 81 (2013), 225-236. doi: 10.1007/s12043-013-0565-9.  Google Scholar

[16]

Journal of Applied Fluid Mechanics, 8 (2015), 207-212. Google Scholar

[17]

Journal of Applied Fluid Mechanics, 7 (2014), 357-366. Google Scholar

[18]

World Applied Science Journal, 13 (2011), 662-666. Google Scholar

[19]

Communications in Nonlinear Science and Numerical Simulations, 17 (2012), 1493-1499. doi: 10.1016/j.cnsns.2011.09.023.  Google Scholar

[20]

Applied Mathematical Modelling, 35 (2011), 3991-3997. doi: 10.1016/j.apm.2011.02.001.  Google Scholar

[21]

Ain Shams Engineering Journal, 4 (2013), 493-499. doi: 10.1016/j.asej.2012.10.002.  Google Scholar

[22]

Journal of King Saud University- Science, 26 (2014), 75-78. doi: 10.1016/j.jksus.2013.07.001.  Google Scholar

[23]

Communications in Nonlinear Science and Numerical Simulations, 14 (2009), 1810-1815. doi: 10.1016/j.cnsns.2008.07.009.  Google Scholar

[24]

Applied Mathematics and Computation, 207 (2009), 279-282. doi: 10.1016/j.amc.2008.10.031.  Google Scholar

[25]

Canadian Journal of Physics, 89 (2011), 979-984. doi: 10.1139/p11-083.  Google Scholar

[26]

Physics Letters A, 372 (2008), 417-423. doi: 10.1016/j.physleta.2007.07.051.  Google Scholar

[27]

Applied Mathematics and Computation, 204 (2008), 162-169. doi: 10.1016/j.amc.2008.06.011.  Google Scholar

[28]

Nonlinear Analysis: Modelling and Control, 17 (2012), 369-378.  Google Scholar

[29]

Applied Mathematics and Computation, 212 (2009), 1-13. doi: 10.1016/j.amc.2009.02.009.  Google Scholar

[30]

International Journal of Computer Mathematics, 87 (2010), 1716-1725. doi: 10.1080/00207160802450166.  Google Scholar

show all references

References:
[1]

Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 734-748. doi: 10.1016/j.cnsns.2007.12.004.  Google Scholar

[2]

Romanian Journal of Physics, 58 (2013), 729-748.  Google Scholar

[3]

Advanced Studies in Theoretical Physics, 2 (2008), 787-794.  Google Scholar

[4]

Applied Mathematics and Computation, 214 (2009), 645-647. doi: 10.1016/j.amc.2009.04.001.  Google Scholar

[5]

Applied Mathematics and Computation, 217 (2010), 1771-1773. doi: 10.1016/j.amc.2009.09.042.  Google Scholar

[6]

Journal of Applied Fluid Mechanics, 7 (2014), 603-609. Google Scholar

[7]

Romaninan Reports in Physics, 65 (2013), 27-62. Google Scholar

[8]

Journal of Modern Optics, 60 (2013), 1627-1636. doi: 10.1080/09500340.2013.850777.  Google Scholar

[9]

European Physical Journal, Plus, 128 (2013), p140. Google Scholar

[10]

Nonlinear Dynamics, 66 (2011), 497-507. doi: 10.1007/s11071-010-9928-7.  Google Scholar

[11]

Journal of Applied Fluid Mechanics, 6 (2013), 339-350. Google Scholar

[12]

Journal of Applied Fluid Mechanics, 7 (2014), 711-718. Google Scholar

[13]

Computational and Applied Mathematics, 33 (2014), 831-839. doi: 10.1007/s40314-013-0098-3.  Google Scholar

[14]

Pramana, 81 (2013), 225-236. Google Scholar

[15]

Pramana, 81 (2013), 225-236. doi: 10.1007/s12043-013-0565-9.  Google Scholar

[16]

Journal of Applied Fluid Mechanics, 8 (2015), 207-212. Google Scholar

[17]

Journal of Applied Fluid Mechanics, 7 (2014), 357-366. Google Scholar

[18]

World Applied Science Journal, 13 (2011), 662-666. Google Scholar

[19]

Communications in Nonlinear Science and Numerical Simulations, 17 (2012), 1493-1499. doi: 10.1016/j.cnsns.2011.09.023.  Google Scholar

[20]

Applied Mathematical Modelling, 35 (2011), 3991-3997. doi: 10.1016/j.apm.2011.02.001.  Google Scholar

[21]

Ain Shams Engineering Journal, 4 (2013), 493-499. doi: 10.1016/j.asej.2012.10.002.  Google Scholar

[22]

Journal of King Saud University- Science, 26 (2014), 75-78. doi: 10.1016/j.jksus.2013.07.001.  Google Scholar

[23]

Communications in Nonlinear Science and Numerical Simulations, 14 (2009), 1810-1815. doi: 10.1016/j.cnsns.2008.07.009.  Google Scholar

[24]

Applied Mathematics and Computation, 207 (2009), 279-282. doi: 10.1016/j.amc.2008.10.031.  Google Scholar

[25]

Canadian Journal of Physics, 89 (2011), 979-984. doi: 10.1139/p11-083.  Google Scholar

[26]

Physics Letters A, 372 (2008), 417-423. doi: 10.1016/j.physleta.2007.07.051.  Google Scholar

[27]

Applied Mathematics and Computation, 204 (2008), 162-169. doi: 10.1016/j.amc.2008.06.011.  Google Scholar

[28]

Nonlinear Analysis: Modelling and Control, 17 (2012), 369-378.  Google Scholar

[29]

Applied Mathematics and Computation, 212 (2009), 1-13. doi: 10.1016/j.amc.2009.02.009.  Google Scholar

[30]

International Journal of Computer Mathematics, 87 (2010), 1716-1725. doi: 10.1080/00207160802450166.  Google Scholar

[1]

Yuanqing Xu, Xiaoxiao Zheng, Jie Xin. New explicit and exact traveling wave solutions of (3+1)-dimensional KP equation. Mathematical Foundations of Computing, 2021  doi: 10.3934/mfc.2021006

[2]

Sel Ly, Nicolas Privault. Stochastic ordering by g-expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 61-98. doi: 10.3934/puqr.2021004

[3]

Mingshang Hu, Shige Peng. G-Lévy processes under sublinear expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 1-22. doi: 10.3934/puqr.2021001

[4]

Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035

[5]

Chiun-Chuan Chen, Hung-Yu Chien, Chih-Chiang Huang. A variational approach to three-phase traveling waves for a gradient system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021055

[6]

Wensheng Yin, Jinde Cao, Guoqiang Zheng. Further results on stabilization of stochastic differential equations with delayed feedback control under $ G $-expectation framework. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021072

[7]

Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steady-state and first passage time distributions for waiting times in the $ MAP/M/s+G $ queueing model with generally distributed patience times. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021078

[8]

Andrew Comech, Elena Kopylova. Orbital stability and spectral properties of solitary waves of Klein–Gordon equation with concentrated nonlinearity. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021063

[9]

Yohei Yamazaki. Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3579-3614. doi: 10.3934/dcds.2021008

[10]

Woocheol Choi, Youngwoo Koh. On the splitting method for the nonlinear Schrödinger equation with initial data in $ H^1 $. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3837-3867. doi: 10.3934/dcds.2021019

[11]

Amanda E. Diegel. A C0 interior penalty method for the Cahn-Hilliard equation. Electronic Research Archive, , () : -. doi: 10.3934/era.2021030

[12]

Haili Qiao, Aijie Cheng. A fast high order method for time fractional diffusion equation with non-smooth data. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021073

[13]

Dmitry Treschev. Travelling waves in FPU lattices. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 867-880. doi: 10.3934/dcds.2004.11.867

[14]

Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973

[15]

Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817

[16]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189

[17]

Yu Yang, Jinling Zhou, Cheng-Hsiung Hsu. Critical traveling wave solutions for a vaccination model with general incidence. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021087

[18]

Pascal Noble, Sebastien Travadel. Non-persistence of roll-waves under viscous perturbations. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 61-70. doi: 10.3934/dcdsb.2001.1.61

[19]

Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, 2021, 15 (3) : 445-474. doi: 10.3934/ipi.2020075

[20]

Yinsong Bai, Lin He, Huijiang Zhao. Nonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021049

2019 Impact Factor: 1.233

Metrics

  • PDF downloads (108)
  • HTML views (0)
  • Cited by (10)

[Back to Top]