scholarly journals The Mass Calculation of Solitary Wave Solution of the One-Dimensional Burgers Equation

POSITRON ◽  
2012 ◽  
Vol 2 (1) ◽  
Author(s):  
Teguh B. Prayitno
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Lagrangian Density ◽  
Burgers Equation ◽  
Solitary Wave Solution ◽  
Classical Field Theory ◽  
Classical Field ◽  
Hamiltonian Density ◽  
One Dimensional ◽  
The One

We have calculated the mass of the solitary wave solution of the one-dimensional Burgers equation by integrating the Hamiltonian density of its equation based on the formulation of the classical field theory. To use this method, we first construct the Lagrangian density in order to obtain the Hamiltonian density by initially introducing the ansatz function of the appropriate field. In this paper, we have obtained that the mass of the solitary of the one-dimensional of Burgers equation is literally divergent.

Solitary-wave solution for a complex one-dimensional field

1976 ◽  
Vol 59 (4) ◽  
pp. 255-258 ◽  
Author(s):  
S. Sarker ◽  
S.E. Trullinger ◽  
A.R. Bishop
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
One Dimensional

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

The novel multi-solitary wave solution to the fifth-order KdV equation

2004 ◽  
Vol 13 (10) ◽  
pp. 1606-1610 ◽  
Author(s):  
Zhang Yi ◽  
Chen Deng-Yuan
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
The Novel ◽  
Fifth Order

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

Emerson's Atom and the Matter of Suffering

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble
Keyword(s):  
Field Theory ◽  
Natural History ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Other ◽  
History Of ◽  
The One ◽  
The Individual ◽  
Solid Bodies ◽  
Lines Of Force

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.

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