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JournalISSN: 1007-5704

Communications in Nonlinear Science and Numerical Simulation 

About: Communications in Nonlinear Science and Numerical Simulation is an academic journal. The journal publishes majorly in the area(s): Nonlinear system & Fractional calculus. It has an ISSN identifier of 1007-5704. Over the lifetime, 6084 publication(s) have been published receiving 140808 citation(s).
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Abstract: We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a single mathematically tractable equation from which the main characteristics of the considered curves can be deduced. We focus on the effects of the involved parameters through both analytical results and computational evaluations.

Journal ArticleDOI
Abstract: In this paper, we mainly investigate a (2+1)-dimensional coupled nonlinear partial differential equation with variable coefficients in an inhomogeneous medium. Based on the Hirota bilinear form and symbolic computation, the breather wave solutions and lump solutions are constructed by using the extended homoclinic breather technique and the generalized positive quadratic function method. Also, Hirota bilinear method is applied to considered equation for finding N-soliton wave solutions. When the coefficients of the equation are different, the corresponding improved results are obtained for some special equations. Furthermore, by plotting the images of different types of solutions, their dynamic behaviors are analyzed.

Journal ArticleDOI
T.S. Moretlo1, T.S. Moretlo2, A.R. Adem3, Ben Muatjetjeja4  +1 moreInstitutions (4)
TL;DR: A generalized BKP equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed and can well mimic complex waves and their dealing dynamics in fluids.
Abstract: A generalized ( 1 + 2 )-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–Petviashvili equation is ambassador of the higher dimensional Kadomtsev–Petviashvili hierarchy. This equation was acquired by a diminution for the well-known three-dimensional Kadomtsev–Petviashvili equation which illustrates the dissemination of nonlinear waves in plasmas and fluid dynamics. We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method. Finally, we compute conserved currents courtesy using the invariance and multiplier technique. The findings can well mimic complex waves and their dealing dynamics in fluids.

Journal ArticleDOI
Abstract: Normally hyperbolic invariant manifolds theory provides an efficient tool for proving diffusion in dynamical systems. In this paper we develop a methodology for computer assisted proofs of diffusion in a-priori chaotic systems based on this approach. We devise a method, which allows us to validate the needed conditions in a finite number of steps, which can be performed by a computer by means of rigorous-interval-arithmetic computations. We apply our method to the generalized standard map, obtaining diffusion over an explicit range of actions.

Journal ArticleDOI
Abstract: We consider an electron in an atom driven by an infrared (IR) elliptically polarized laser field after its ionization by an ultrashort extreme ultraviolet (XUV) pulse. We find that, regardless of the atom species and the laser ellipticity, there exists XUV parameters for which the electron returns to its parent ion after ionizing, i.e., undergoes a recollision. This shows that XUV pulses trigger efficiently recollisions in atoms regardless of the ellipticity of the IR field. The XUV parameters for which the electron undergoes a recollision are obtained by studying the location of recolliding periodic orbits (RPOs) in phase space. The RPOs and their linear stability are followed and analyzed as a function of the intensity and ellipticity of the IR field. We determine the relation between the RPOs identified here and the ones found in the literature and used to interpret other types of highly nonlinear phenomena for low elliptically and circularly polarized IR fields.

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