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  • World Scientific Pub Co Pte Ltd  (5)
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  • World Scientific Pub Co Pte Ltd  (5)
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  • 1
    Online Resource
    Online Resource
    Nonautonomous solitons in terms of the double Wronskian determinant for a variable-coefficient Gross–Pitaevskii equation in the Bose–Einstein condensate
    World Scientific Pub Co Pte Ltd ; 2016
    In:  Modern Physics Letters B Vol. 30, No. 09 ( 2016-04-10), p. 1650103-
    Details
    In: Modern Physics Letters B, World Scientific Pub Co Pte Ltd, Vol. 30, No. 09 ( 2016-04-10), p. 1650103-
    Abstract: Under investigation in this paper is a variable-coefficient Gross–Pitaevskii equation which describes the Bose–Einstein condensate. Lax pair, bilinear forms and bilinear Bäcklund transformation for the equation under some integrable conditions are derived. Based on the Lax pair and bilinear forms, double Wronskian solutions are constructed and verified. The [Formula: see text]th-order nonautonomous solitons in terms of the double Wronskian determinant are given. Propagation and interaction for the first- and second-order nonautonomous solitons are discussed from three cases. Amplitudes of the first- and second-order nonautonomous solitons are affected by a real parameter related to the variable coefficients, but independent of the gain-or-loss coefficient [Formula: see text] and linear external potential coefficient [Formula: see text]. For Case 1 [Formula: see text] , [Formula: see text] leads to the accelerated propagation of nonautonomous solitons. Parabolic-, cubic-, exponential- and cosine-type nonautonomous solitons are exhibited due to the different choices of [Formula: see text] . For Case 2 [Formula: see text], if the real part of the spectral parameter equals 0, stationary soliton can be formed. If we take the harmonic external potential coefficient [Formula: see text] as a positive constant and let the real parts of the two spectral parameters be the same, bound-state-like structures can be formed, but there are only one attractive and two repulsive procedures. For Case 3 [[Formula: see text] and [Formula: see text] are taken as nonzero constants], head-on interaction, overtaking interaction and bound-state structure can be formed based on the signs of the two spectral parameters.
    Type of Medium: Online Resource
    ISSN: 0217-9849 , 1793-6640
    URL: Article
    DOI: 10.1142/S0217984916501037
    RVK:
    UA 5534.B
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2016
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    Online Resource
  • 2
    Online Resource
    Online Resource
    Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev–Petviashvili equation in the fluid/plasma mechanics
    World Scientific Pub Co Pte Ltd ; 2016
    In:  Modern Physics Letters B Vol. 30, No. 25 ( 2016-09-20), p. 1650265-
    Details
    In: Modern Physics Letters B, World Scientific Pub Co Pte Ltd, Vol. 30, No. 25 ( 2016-09-20), p. 1650265-
    Abstract: Under investigation in this paper is a (2[Formula: see text]+[Formula: see text] 1)-dimensional B-type Kadomtsev–Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic–elastic interactions imply that the interaction between the inelastic region and another one is elastic.
    Type of Medium: Online Resource
    ISSN: 0217-9849 , 1793-6640
    URL: Article
    DOI: 10.1142/S0217984916502651
    RVK:
    UA 5534.B
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2016
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  • 3
    Online Resource
    Online Resource
    Bilinear forms and dark-soliton solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber
    World Scientific Pub Co Pte Ltd ; 2016
    In:  Modern Physics Letters B Vol. 30, No. 24 ( 2016-09-10), p. 1650312-
    Details
    In: Modern Physics Letters B, World Scientific Pub Co Pte Ltd, Vol. 30, No. 24 ( 2016-09-10), p. 1650312-
    Abstract: In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation is investigated, which describes the propagation of the attosecond pulses in an optical fiber. Via the Hirota’s method and auxiliary functions, bilinear forms and dark one-, two- and three-soliton solutions are obtained. Propagation and interaction of the solitons are discussed graphically: We observe that the solitonic velocities are only related to [Formula: see text], [Formula: see text] , [Formula: see text] and [Formula: see text] , the coefficients of the second-, third-, fourth- and fifth-order terms, respectively, with [Formula: see text] being the scaled distance, while the solitonic amplitudes are related to [Formula: see text] , [Formula: see text], [Formula: see text] , [Formula: see text] as well as the wave number. When [Formula: see text] , [Formula: see text], [Formula: see text] and [Formula: see text] are the constants, or the linear, quadratic and trigonometric functions of [Formula: see text] , we obtain the linear, parabolic, cubic and periodic dark solitons, respectively. Interactions between (among) the two (three) solitons are depicted, which can be regarded to be elastic because the solitonic amplitudes remain unchanged except for some phase shifts after each interaction in an optical fiber.
    Type of Medium: Online Resource
    ISSN: 0217-9849 , 1793-6640
    URL: Article
    DOI: 10.1142/S0217984916503127
    RVK:
    UA 5534.B
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2016
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  • 4
    Online Resource
    Online Resource
    Research on the dissipative characteristics of unsteady heat conduction for the one-dimensional sphere
    World Scientific Pub Co Pte Ltd ; 2018
    In:  Modern Physics Letters B Vol. 32, No. 25 ( 2018-09-10), p. 1850293-
    Details
    In: Modern Physics Letters B, World Scientific Pub Co Pte Ltd, Vol. 32, No. 25 ( 2018-09-10), p. 1850293-
    Abstract: In this paper, the dissipative characteristics of unsteady heat conduction process for the one-dimensional sphere is studied. The dissipation function can be regarded as a Lyapunov function for the heat conduction system, which determines the evolution direction of the system and the stability of the steady state. By use of the vector formula, the relationship between the thermal potential and dissipation function is derived, and its similarity with the dissipation system of mechanical energy is shown. The expression of dissipation function is obtained when the boundary temperature is fixed. In addition, an example for optimization of heat conduction process is discussed based on the entransy dissipation extremum principle.
    Type of Medium: Online Resource
    ISSN: 0217-9849 , 1793-6640
    URL: Article
    DOI: 10.1142/S0217984918502937
    RVK:
    UA 5534.B
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2018
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  • 5
    Online Resource
    Online Resource
    Taiji program in space for gravitational universe with the first run key technologies test in Taiji-1
    World Scientific Pub Co Pte Ltd ; 2021
    In:  International Journal of Modern Physics A Vol. 36, No. 11n12 ( 2021-04-30), p. 2102002-
    Details
    In: International Journal of Modern Physics A, World Scientific Pub Co Pte Ltd, Vol. 36, No. 11n12 ( 2021-04-30), p. 2102002-
    Type of Medium: Online Resource
    ISSN: 0217-751X , 1793-656X
    URL: Article
    DOI: 10.1142/S0217751X21020024
    RVK:
    UA 4381
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2021
    SSG: 16,12
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