English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A general theory for the existence of solitary wave and double layer at M= Mchas been discussed, where Mc is the lower bound of the Mach number M, i.e.,solitary wave and/or double layer solutions of the well-known energy integralstart to exist for M> Mc. Ten important theorems have been proved to confirmthe existence of solitary wave and double layer at M = Mc. IfV({\phi})({\equiv}V(M,{\phi})) denotes the Sagdeev potential with {\phi} is theperturbed field or perturbed dependent variable associated with the specificproblem, V(M,{\phi}) is well defined as a real number for all M {\in}\mathcal{M} and for all {\phi} {\in} {\Phi}, and V(M,0)=V'(M,0)=V"(Mc,0)=0,V"'(Mc,0)<0 (V"'(Mc,0)>0), \deltaV/\deltaM < 0 for all M({\in} \mathcal{M}) > 0and for all {\phi}({\in} {\Phi}) > 0 ({\phi}({\in}{\Phi}) < 0), where "'{\equiv} \delta/\delta{\phi} ", the main analytical results for the existenceof solitary wave and double layer solution of the energy integral at M= Mc areas follows. Result-1: If there exists at least one value M0 of M such that thesystem supports positive (negative) potential solitary waves for all Mc<M<M0,then there exist either a positive (negative) potential solitary wave or apositive (negative) potential double layer at M= Mc. Result-2: If the systemsupports only negative (positive) potential solitary waves for M> Mc, thenthere does not exist positive (negative) potential solitary wave at M= Mc.Result-3: It is not possible to have coexistence of both positive and negativepotential solitary structures (including double layers) at M= Mc. Apart fromthe conditions of Result-1, the double layer solution at M= Mc is possible onlywhen there exists a double layer solution in any right neighborhood of Mc.Finally these analytical results have been applied to a specific problem ondust acoustic waves in nonthermal plasma in search of new results.

An analytical study on the existence of solitary wave and double layer solution of the well-known energy integral at M= Mc