In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial basis function network method. Previously, we obtained single-step spinning solutions of the equation using the Galerkin method. First, we verify the numerical solver through an exact solution of a forced version of the equation. Doing so, we compare the numerical results obtained for different space and time steps with the exact solution. Then, we apply the method to solve the NEP equation and reproduce the previously obtained spinning regimes. In the new series of numerical experiments, we find regimes in the form of spinning trains of steps/kinks comprising one, two, or three kinks. The evolution of the distance between the kinks is analyzed. Two different kinds of boundary conditions are considered: homogeneous and periodic. The dependence of the dynamics on the size of the domain is explored showing how larger domains accommodate multiple spinning fronts. We determine the critical domain size (bifurcation size) above which non-trivial settled regimes become possible. The initial condition determines the direction of motion of the kinks but not their sizes and velocities.
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August 2020
Research Article|
August 04 2020
Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method
Rajeev P. Bhanot
;
Rajeev P. Bhanot
a)
1
School of Chemical Engineering and Physical Sciences, Department of Mathematics, Lovely Professional University
, Phagwara, Punjab 144411, India
2
School of Sciences, Faculty of Health, Engineering and Sciences, University of Southern Queensland
, Toowoomba, Queensland 4350, Australia
a)Author to whom correspondence should be addressed: rajeevbhanot@yahoo.com and rajeev.23674@lpu.co.in
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Dmitry V. Strunin
;
Dmitry V. Strunin
b)
2
School of Sciences, Faculty of Health, Engineering and Sciences, University of Southern Queensland
, Toowoomba, Queensland 4350, Australia
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Duc Ngo-Cong
Duc Ngo-Cong
c)
3
Institute for Advanced Engineering and Space Sciences, University of Southern Queensland
, Toowoomba, Queensland 4350, Australia
4
School of Chemical Engineering, The University of Queensland
, Brisbane, Queensland 4072, Australia
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a)Author to whom correspondence should be addressed: rajeevbhanot@yahoo.com and rajeev.23674@lpu.co.in
b)
Electronic mail: strunin@usq.edu.au
c)
Electronic mail: ngocongduc@gmail.com
Chaos 30, 083119 (2020)
Article history
Received:
March 30 2020
Accepted:
July 10 2020
Citation
Rajeev P. Bhanot, Dmitry V. Strunin, Duc Ngo-Cong; Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method. Chaos 1 August 2020; 30 (8): 083119. https://doi.org/10.1063/5.0009215
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