Variable separation solutions of the Wick-type stochastic Broer–Kaup system

2012 ◽  
Vol 90 (9) ◽  
pp. 871-876
Author(s):  
Cuiyun Liu ◽  
Yueyue Wang ◽  
Chaoqing Dai
Keyword(s):  
White Noise ◽  
Variable Separation ◽  
Noise Environment ◽  
Localized Structures ◽  
Hermite Transformation

With the help of Hermite transformation, we obtain variable separation solutions of the Wick-type stochastic Broer–Kaup system in the white noise environment. These variable separation solutions are more general than travelling solutions reported in the literature. To illustrate the novelty of variable separation solutions, we present some localized structures with chaotic behaviors.

The Effects of White Noise on Sleep and Duration in Individuals Living in a High Noise Environment in New York City

2021 ◽  
Author(s):  
Matthew R. Ebben ◽  
Peter Yan ◽  
Ana C. Krieger
Keyword(s):  
New York ◽  
New York City ◽  
White Noise ◽  
York City ◽  
High Noise ◽  
Noise Environment

Folded Solitary Waves and Foldons in the (2+1)-Dimensional Long Dispersive Wave Equation

2003 ◽  
Vol 58 (5-6) ◽  
pp. 280-284
Author(s):  
J.-F. Zhang ◽  
Z.-M. Lu ◽  
Y.-L. Liu
Keyword(s):  
Wave Equation ◽  
Solitary Waves ◽  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Dispersive Wave ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Dispersive Wave Equation ◽  
03.65 Ge

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)- dimensional long dispersive wave equation: λqt + qxx − 2q ∫ (qr)xdy = 0, λrt − rxx + 2r ∫ (qr)xdy= 0, is derived. In addition to some types of the usual localized structures such as dromion, lumps, ring soliton and oscillated dromion, breathers soliton, fractal-dromion, peakon, compacton, fractal and chaotic soliton structures can be constructed by selecting the arbitrary single valued functions appropriately, a new class of localized coherent structures, that is the folded solitary waves and foldons, in this system are found by selecting appropriate multi-valuded functions. These structures exhibit interesting novel features not found in one-dimensions. - PACS: 03.40.Kf., 02.30.Jr, 03.65.Ge.

A New Class of (2+1)-Dimensional Combined Structures with Completely Elastic and Non-Elastic Interactive Properties

2006 ◽  
Vol 61 (1-2) ◽  
pp. 53-59 ◽  
Author(s):  
Cheng-Lin Bai ◽  
Cheng-Jie Bai ◽  
Hong Zhao
Keyword(s):  
Solitary Waves ◽  
Balance Method ◽  
Physical Models ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

Taking the new (2+1)-dimensional generalized Broer-Kaup system as an example, we obtain an exact variable separation excitation which can describe some quite universal (2+1)-dimensional physical models, with the help of the extended homogeneous balance method. Based on the derived excitation, a new class of combined structures, i. e., semifolded solitary waves and semifoldons, is defined and studied. The interactions of the semifolded localized structures are illustrated both analytically and graphically. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik

New Exact Solutions and Fractal Localized Structures for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2005 ◽  
Vol 60 (4) ◽  
pp. 245-251 ◽  
Author(s):  
Jian-Ping Fang ◽  
Qing-Bao Ren ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Coherent Structures ◽  
Variable Separation ◽  
Wave Excitation ◽  
Interesting Phenomenon ◽  
New Exact Solutions ◽  
Localized Structures ◽  
Fractal Properties ◽  
New Type ◽  
03.65 Ge

Abstract In this work, a novel phenomenon that localized coherent structures of a (2+1)-dimensional physical model possess fractal properties is discussed. To clarify this interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) system as a concrete example. First, with the help of an extended mapping approach, a new type of variable separation solution with two arbitrary functions is derived. Based on the derived solitary wave excitation, we reveal some special regular fractal and stochastic fractal solitons in the (2+1)-dimensional BLP system. - PACS: 05.45.Yv, 03.65.Ge

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

2002 ◽  
Vol 57 (12) ◽  
pp. 929-936 ◽  
Author(s):  
Ji Lin ◽  
Hua-mei Li
Keyword(s):  
Phase Shift ◽  
Coherent Structures ◽  
Higher Order ◽  
Separation Method ◽  
Variable Separation ◽  
Localized Structures ◽  
Painlevé Property ◽  
Variable Separation Method ◽  
Truncated Painlevé Expansion

It is proven that the (2+1) dimensional higher-order Broer-Kaup system the possesses the Painlevé property, using the Weiss-Tabor-Carnevale method and Kruskal’s simplification. Abundant localized coherent structures are obtained by using the standard truncated Painlevé expansion and the variable separation method. Fractal dromion solutions and multi-peakon structures are discussed. The interactions of three peakons are investigated. The interactions among the peakons are not elastic; they interchange their shapes but there is no phase shift

Re-study on localized structures based on variable separation solutions from the modified tanh-function method

2015 ◽  
Vol 83 (3) ◽  
pp. 1331-1339 ◽  
Author(s):  
Yue-Yue Wang ◽  
Yu-Peng Zhang ◽  
Chao-Qing Dai
Keyword(s):  
Function Method ◽  
Variable Separation ◽  
Localized Structures

scholarly journals Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

2018 ◽  
Vol 22 (4) ◽  
pp. 1781-1786 ◽  
Author(s):  
Zitian Li
Keyword(s):  
Symbolic Computation ◽  
Coherent Structures ◽  
Vries Equation ◽  
Qualitative Behavior ◽  
Variable Separation ◽  
Wave Type ◽  
Localized Structures ◽  
Mapping Approach ◽  
De Vries ◽  
Rouge Wave

With the aid of symbolic computation, we derive new types of variable separation solutions for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation based on an improved mapping approach. Rich coherent structures like the soliton-type, rouge wave-type, and cross-like fractal type structures are presented, and moreover, the fusion interactions of localized structures are graphically investigated. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized.

scholarly journals 0379 The Effect of White Noise on Individuals Complaining of Poor Quality Sleep in a High Noise Environment in New York City

SLEEP ◽  
2018 ◽  
Vol 41 (suppl_1) ◽  
pp. A145-A145
Author(s):  
M R Ebben ◽  
M Q Degrazia ◽  
A C Krieger
Keyword(s):  
New York ◽  
New York City ◽  
White Noise ◽  
York City ◽  
Poor Quality ◽  
High Noise ◽  
Noise Environment ◽  
Quality Sleep

Localized Coherent Soliton Structures in a Generalized (2+1)-Dimensional Nonlinear Schrödinger System

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4407-4414 ◽  
Author(s):  
Chun-Long Zheng ◽  
Zheng-Mao Sheng
Keyword(s):  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger ◽  
Localized Structures ◽  
Nonlinear Schrödinger System ◽  
Localized Excitations ◽  
Schrödinger System ◽  
Variable Separation Approach

A variable separation approach is used to obtain localized coherent structures in a generalized (2+1)-dimensional nonlinear Schrödinger system. Applying a special Bäcklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this system are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, peakons, breathers and instantons are constructed.

NEW SOLITARY WAVE AND JACOBI PERIODIC WAVE EXCITATIONS IN (2+1)-DIMENSIONAL BOITI–LEON–MANNA–PEMPINELLI SYSTEM

2008 ◽  
Vol 22 (15) ◽  
pp. 2407-2420 ◽  
Author(s):  
CHENG-JIE BAI ◽  
HONG ZHAO
Keyword(s):  
General Solution ◽  
Solitary Wave ◽  
Elliptic Functions ◽  
Periodic Wave ◽  
Jacobi Elliptic Functions ◽  
Variable Separation ◽  
Smooth Functions ◽  
Localized Structures ◽  
Variable Separation Approach ◽  
Lower Dimensional

By means of the multilinear variable separation approach, a general variable separation solution of the Boiti–Leon–Manna–Pempinelli equation is derived. Based on the general solution, some new types of localized structures — compacton and Jacobi periodic wave excitations are obtained by introducing appropriate lower-dimensional piecewise smooth functions and Jacobi elliptic functions.

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