THERMAL SCIENCE
International Scientific Journal
STUDYING ON KUDRYASHOV-SINELSHCHIKOV DYNAMICAL EQUATION ARISING IN MIXTURES LIQUID AND GAS BUBBLES
ABSTRACT
In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov non-linear PDE are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted.
KEYWORDS
PAPER SUBMITTED: 2020-03-31
PAPER REVISED: 2021-08-01
PAPER ACCEPTED: 2021-08-06
PUBLISHED ONLINE: 2021-09-04
THERMAL SCIENCE YEAR
2022, VOLUME
26, ISSUE
Issue 2, PAGES [1229 - 1244]
- Kudryashov, N. A., Sinelshchikov, D. I., Nonlinear wave in bubbly liquids with consideration for viscosity and heat transfer, Phys. Lett. A, 374(2010), pp. 2011-2016
- Kudryashov, N. A., Sinelshchikov, D. I., Nonlinear evolution equation for describing waves in bubbly liquids with viscosity and heat transfer consideration, Appl. Math. Comput., 217(2010), pp. 414-421
- Lu, J., New exact solutions for Kudryashov-Sinelshchikov equation, Advances in Difference Equations, 2018(2018), 1, p. 374
- Ryabov, P. N., Exact solutions of the Kudryashov-Sinelshchikov equation, Applied Mathematics and Computation, 217(2010), 7, pp. 3585-3590
- Tu, J. M., et al., On Lie symmetries, optimal systems and explicit solutions to the Kudryashov-Sinelshchikov equation, Applied Mathematics and Computation, 275(2016), pp. 345-352
- Zhao, Y. M., F-expansion method and its application for finding new exact solutions to the Kudryashov-Sinelshchikov equation, Journal of Applied Mathematics, 2013(2013)
- Inc, M. et al., New solitary wave solutions and conservation laws to the Kudryashov-Sinelshchikov equation, Optik, 142(2017), pp. 665-673
- Vitanov, N. K., Application of simplest equations of Bernoulli and Riccati kind for obtaining exact travelingwave solutions for a class of PDEs with polynomial nonlinearity, Communications in Nonlinear Science and Numerical Simulation, 15(2010), 8, pp. 2050-2060
- Vitanov, N. K., On modified method of simplest equation for obtaining exact solutions of nonlinear PDEs: case of elliptic simplest equation, Pliska Studia Mathematica Bulgarica, 21(2012), 1, pp. 257-266
- Bulut, H., et al., On the prototype solutions of symmetric regularized long wave equation by generalized Kudryashov method, Math. Lett., 1(2015), 2, pp. 10-16
- Baskonus, H., Bulut, H., New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics, Entropy, 17(2015), 6, pp. 4255-4270
- Li, J., Chen, G., Exact traveling wave solutions and their bifurcations for the Kudryashov-Sinelshchikov equation, International Journal of Bifurcation and Chaos, 22(2012), 05, 1250118
- Baskonus, H. M., Complex soliton solutions to the Gilson-Pickering Model, Axioms, 8(2019), 1, p. 18
- Baskonus, H. M., On the Dark and Bright Solitons to the Negative-Order Breaking Soliton Model with (2+1)-Dimensional, In International workshop of Mathematical Modelling, Applied Analysis and Computation, Springer, Singapore, 2018, pp. 229-242
- Vitanov, N. K., Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs, Communications in Nonlinear Science and Numerical Simulation, 16(2011), 3, pp. 1176-1185
- Yokus, A., et al., Numerical simulation and solutions of the two-component second order KdV evolutionary system, Numerical Methods for Partial Differential Equations, 34(2018), 1, pp. 211-227
- Baskonus, H. M., et al., New complex hyperbolic structures to the Lonngren-wave equation by using sine-Gordon expansion method, Applied Mathematics and Nonlinear Sciences, 4(2019), 1, pp. 129-138
- He, B., et al., The bifurcation and exact peakons, solitary and periodic wave solutions for the Kudryashov-Sinelshchikov equation, Communications in Nonlinear Science and Numerical Simulation, 17(2012), 11, pp. 4137-4148
- Randrüüt, M., Braun, M., On identical traveling-wave solutions of the Kudryashov-Sinelshchikov and related equations, International Journal of Non-Linear Mechanics, 58(2014), pp. 206-211
- He, Y., et al., A improved F-expansion method and its application to Kudryashov-Sinelshchikov equation, Mathematical Methods in the Applied Sciences, 37(2014), 12, pp. 1717-1722
- Yang, H., et al., Lie symmetry analysis and exact explicit solutions of three-dimensional Kudryashov-Sinelshchikov equation, Communications in Nonlinear Science and Numerical Simulation, 27(2015), 1-3, pp. 271-280
- He, Y., New Jacobi elliptic function solutions for the Kudryashov-Sinelshchikov-equation using improved Fexpansion method, Mathematical Problems in Engineering, 2013(2013)
- Gupta, A. K., Ray, S. S., On the solitary wave solution of fractional Kudryashov-Sinelshchikov equation describing nonlinear wave processes in a liquid containing gas bubbles, Applied Mathematics and Computation, 298(2017), pp. 1-12
- He, Y., Exact solutions of the Kudryashov-Sinelshchikov equation by modified exp-function method, International Mathematical Forum, 8(2013), 18, pp. 895-902
- Zhou, A. J., Chen, A. H., Exact solutions of the Kudryashov-Sinelshchikov equation in ideal liquid with gas bubbles, Physica Scripta, 93(2018), 12, pp. 125-201
- Seadawy, A. R., et al., Nonlinear wave solutions of the Kudryashov-Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity, Journal of Taibah University for Science, 13(2019), 1, pp. 1060-1072
- Shu, J. J., The proper analytical solution of the Korteweg-de Vries-Burgers equation, arXivpreprint arXiv:1403.3636., (2014)
- Vitanov, N. K., et al., Application of the method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg-de Vries equation and generalized Camassa-Holm equation, Applied Mathematics and Computation, 219(2013), 14, pp. 7480-7492