An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinea

A foldable stand for a bassinet or the like has four upright legs in a rectangular configuration when unfolded. At each end of the stand, the legs are rigidly interconnected by a horizontal bar supporting the corresponding end of the bassinet. Above the support bars at opposite ends of the stand, opposed U-shaped guard rails are pivotally mounted to the tops of the legs such that when deployed the guard rails bracket the lower ends of the bassinet. A diagonal cross brace is pivotally connected at one end to a point near the bottom of each leg and at the other end to the end of the U-shaped guard rail which is connected to the top of the corresponding leg on the same side of the stand. There are four such cross braces, two of which crisscross on each side of the stand and are pivotally interconnected like scissors so that the two end pairs of legs can be collapsed toward each other while remaining parallel as the cross braces close and the guard rails tip upright. Stops are located on the cross braces to lock the stand when the guard rails are horizontal.

[1]  A. Roy Chowdhury,et al.  Normal form analysis and chaotic scenario in a Schrödinger-Boussinesq system , 2002 .

[2]  Ruoxia Yao,et al.  New exact solutions for three nonlinear evolution equations , 2002 .

[3]  En-Gui Fan,et al.  Traveling wave solutions for nonlinear equations using symbolic computation , 2002 .

[4]  M. Salerno,et al.  Soliton ratchets. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Mingliang Wang,et al.  Exact Solitary wave and Soliton solutions of the fifth order model equation , 2002 .

[6]  Scott A. Yost,et al.  A multiple grid approach for open channel flows with strong shocks , 2001, Appl. Math. Comput..

[7]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[8]  Yuri N. Fedorov,et al.  Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians , 2001 .

[9]  L. Borcea.  A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency , 2001 .

[10]  D. Koelle,et al.  Josephson vortex in a ratchet potential: theory. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[12]  Engui Fan,et al.  Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation , 2000 .

[13]  Woo-Pyo Hong,et al.  New solitonic solutions to a (3+1)-dimensional Jimbo-Miwa equation , 2000 .

[14]  K. Toda,et al.  Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2+1)-Dimensional Equation , 2000, math/0001188.

[15]  P. G. Estévez.  Darboux transformation and solutions for an equation in 2+1 dimensions , 1999 .

[16]  D. P. Novikov,et al.  Algebraic-geometric solutions of the Harry Dym equation , 1999 .

[17]  Alexey V. Porubov,et al.  Some general periodic solutions to coupled nonlinear Schrödinger equations , 1999 .

[18]  V. Gani,et al.  Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  N. N. Rao,et al.  Localized nonlinear structures of intense electromagnetic waves in two-electron-temperature electron–positron–ion plasmas , 1999 .

[20]  A. Roy Chowdhury,et al.  Painléve Analysis and Backlund Transformations for Coupled Generalized Schrödinger–Boussinesq Systemfn2 , 1998 .

[21]  A. Samsonov.  On exact quasistationary solutions to a nonlinear reaction-diffusion equation , 1998 .

[22]  N. N. Rao,et al.  Coupled Langmuir and ion-acoustic waves in two-electron temperature plasmas , 1997 .

[23]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[24]  P. Christiansen,et al.  Quasi-periodic solutions of the coupled nonlinear Schrödinger equations , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[25]  M. Moshinsky,et al.  Response to "Comment on 'Penetrability of a one-dimensional Coulomb potential' " by Roger G Newton , 1994 .

[26]  E. J. Parkes,et al.  Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation , 1994 .

[27]  A. Porubov.  Exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid , 1993 .

[28]  Robert Conte,et al.  Link between solitary waves and projective Riccati equations , 1992 .

[29]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[30]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[31]  Willy Hereman,et al.  Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA , 1991 .

[32]  P. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[33]  Ben Silver,et al.  Elements of the theory of elliptic functions , 1990 .

[34]  Peter A. Clarkson,et al.  New similarity reductions and Painleve analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations , 1989 .

[35]  S. Lou,et al.  Deforming some special solutions of the sine-Gordon equation to that of the double sine-Gordon equation , 1989 .

[36]  G. Wilson.  On the quasi-hamiltonian formalism of the KdV equation , 1988 .

[37]  Junkichi Satsuma,et al.  An N-Soliton Solution for the Nonlinear Schrödinger Equation Coupled to the Boussinesq Equation , 1988 .

[38]  M. Boiti,et al.  Spectral transform for a two spatial dimension extension of the dispersive long wave equation , 1987 .

[39]  Alfred Ramani,et al.  Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable? , 1986 .

[40]  Alfred Ramani,et al.  Soliton structure of the Drinfel’d–Sokolov–Wilson equation , 1986 .

[41]  P. Olver.  Applications of Lie Groups to Differential Equations , 1986 .

[42]  B. Kupershmidt,et al.  Mathematics of dispersive water waves , 1985 .

[43]  Yoshimasa Matsuno,et al.  Bilinear Transformation Method , 1984 .

[44]  Charles E. Seyler,et al.  A symmetric regularized‐long‐wave equation , 1984 .

[45]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .

[46]  Gernot Neugebauer,et al.  Einstein-Maxwell solitons , 1983 .

[47]  K. Leung.  Mechanical properties of double-sine-Gordon solitons and the application to anisotropic Heisenberg ferromagnetic chains , 1983 .

[48]  G. Wilson,et al.  The affine lie algebra C(1)2 and an equation of Hirota and Satsuma , 1982 .

[49]  R. Hirota,et al.  Soliton solutions of a coupled Korteweg-de Vries equation , 1981 .

[50]  Antonio Degasperis,et al.  Reduction technique for matrix nonlinear evolution equations solvable by the spectral transform , 1981 .

[51]  Athanassios S. Fokas,et al.  A symmetry approach to exactly solvable evolution equations , 1980 .