Bound states in quantum mechanics must almost always be constructed numerically. One of the best known exceptions concerns the central D−dimensional (often called “anharmonic”) Hamiltonian H = p + a |~r|2 + b |~r|4 + . . . + z |~r|4q+2 (where z = 1) with a complete and elementary solvability at q = 0 (central harmonic oscillator, no free parameters) and with an incomplete, N−level elementary an...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

in this paper, the flow of couple stress fluid is investigated in a helical screw rheometer (hsr). by unwrapping the channel, lands, and the outside rotating barrel, the geometry of hsr is approximated as a shallow infinite channel. both one- and two-dimensional analysis of the problem is presented using rectangular coordinates. in either case an exact solution of the flow problem is presented ...