# On a class of solitary wave solutions of atmospheric nonlinear equations

TL;DR: In this paper, a phase angle function ζ was introduced to study the atmospheric nonlinear equations in the presence of specific forcing and it was shown that the atmospheric equations exhibit the exact and explicit solitary wave solutions under certain conditions.

Abstract: In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.

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TL;DR: In this article , the topographic dynamical effect from Eurasia and North America (NA_Topo) on the winter isentropic meridional mass circulation (IMMC) was investigated using the WACCM.

Abstract: The topographic dynamical effect from Eurasia (EA_Topo) and North America (NA_Topo) on the winter isentropic meridional mass circulation (IMMC) is investigated using the WACCM. The independent effect of EA_Topo and that of NA_Topo, with the former much stronger, are both to strengthen the IMMC that is composed of the lower equatorward cold air branch (CB) and the upper poleward warm air branch in the extratropical tropopshere (WB_TR) and stratosphere (WB_ST). Further investigation of the individual contributions from changes in stationary vs. transient and zonal-mean flow vs. waves reveals that, due to the topography-forced mass redistribution, changes in the low-level meridional pressure gradient force a zonal-mean counter-clockwise/clockwise meridional cell in the southern/northern side of topography. This weakens/strengthens the IMMC south/north of 30° N from the troposphere to lower stratosphere, acting as a dominant contributor to the IMMC changes south of 50° N. Meanwhile, the EA/NA_Topo-forced amplification of stationary waves constructively interacts with those determined by land-sea contrast, making the dominant/minor contributions to the strengthening of CB and WB_TR north of 50° N. The related increase in the upward wave propagation further dominates the WB_ST strengthening in the subpolar region. Meanwhile, transient eddy activities are depressed by EA/NA_Topo along with the weakened background westerly, which partly-offset/dominate-over the contribution from stationary flow in midlatitudes and subpolar region. The coexistence of the other topography (NA/EA_Topo) yields destructive mutual interferrence, which can weaken/offset the independent-EA/NA_Topo-forced meridional mass transport mainly via changing the zonal-mean as well as the downstream wave pattern of mass and meridional wind.

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TL;DR: In this article, a procedure of finding an exact periodic solution for a certain type of nonlinear wave equations with higher-order dispersive term is described, including a case of u t + u u u x - u (5 x ) = 0.

Abstract: A procedure of finding an exact periodic solution for a certain type of nonlinear wave equations is described. The exact solutions for some nonlinear wave equations with higher order dispersive term are explicitly presented including a case of u t + u u x - u (5 x ) =0.

37 citations

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TL;DR: In this article, a coupled nonlinear partial differential equation is studied which represents a model for wave propagation in a one-dimensional nonlinear lattice in the absence of one of the variables.

Abstract: A coupled nonlinear partial differential equation is studied which represents a model for wave propagation in a one-dimensional nonlinear lattice in the absence of one of the variables. The coupled equation is solved exactly by applying the criteria of the Weierstrass elliptic function.

7 citations

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TL;DR: In this article, a procedure for evaluating the forces between classical, charged solitons at large distances is presented, where the SU(2) generalisation of the U(1) symmetric theory is considered.

Abstract: A procedure is offered for evaluating the forces between classical, charged solitons at large distances. This is employed for the solitons of a complex, scalar two-dimensional field theory with a U(1) symmetry, that leads to a conserved chargeQ. These forces are the analogues of the strong interaction forces. The potential,U(Q, R), is found to be attractive, of long range, and strong when the coupling constants in the theory are small. The dependence ofU(Q, R) onQ, the sum of the charges of the two interacting solitons (Q will refer to isospin in the SU(2) generalisation of the U(1) symmetric theory) is of importance in the theory of strong interactions; group theoretical considerations do not give such information. The interaction obtained here will be the leading term in the corresponding quantum field theory when the coupling-constants are small.

3 citations

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TL;DR: In this article, the authors derived the approximate solution by using the function-fitting method for the pseudo-energy function and the existence of the discontinuous periodic solution and the method of function approximation is used.

Abstract: In this paper various non-dispersion solutions of nonlinear waves in the atmosphere are discussed. We turn the nonlinear partial differential equations into the nonlinear ordinary differential equations after the phase angle function has been introduced. The nature around the equilibrium points and singular points of these ordinary differential equations is discussed and various analytic expressions of the nondispersion solutions are obtained. In part (Ⅰ), two problems are dealt with mainly. (ⅰ) The relation between pseudo-energy and the pseudo-energy influence function and nonlinear waves is discussed. Through the discussion of the pseudo-energy influence function, we can determine the existential condition of the periodic solution, the solitary wave solution, the discontinuous periodic solution and the discontinuous solitary wave solution. We also indicate that if there exists an external source, which occasions infinitely small changes in the pseudo-energy influence function, the nonlinear solitary wave can be produced. (ⅱ) The existence of the discontinuous periodic solution is discussed and the method of function approximation is used. In case the analytic solution is unable to be obtained, the approximate solution can be obtained usually by using the Taylor expansion, but this method can bring many troubles. In this paper we derive the approximate solution by using the function-fitting method for the pseudo-energy function. This method avoids the defects of Taylor expansion.

3 citations

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2 citations