To solve quantum mechanical eigenvalue problems using the algorithmic methods recently derived by Nikiforov and Uvarov (1988 Special Functions of Mathematical Physics (Basel: Birkhäuser)) and Ciftci et al (2003 J. Phys. A: Math. Gen. 36 11807), one needs to first convert the associated wave equation into hypergeometric or closely related forms. We point out that once such forms are obtained, the eigenvalue problem can be satisfactorily solved by only imposing the condition that the regular infinite series solutions of the equations should become polynomials, and one need not take recourse to the use of the algorithmic methods. We first demonstrate the directness and simplicity of our approach by dealing with a few case studies and then present new results for the Woods-Saxon potential.

Climate change is an inherent and indispensable component of global development and deliberations on food security and sustainable farm livelihoods. This article attempts to highlight the key issues with regards to climate change, and propounds an approach to upscale holistic and appropriate Climate Smart Agriculture (CSA). The review addresses the climate change impact on, and intricacies of, farm livelihoods, vulnerability and adaptation strategies. Preordained holistic strategies such as CSA can curtail widespread detrimental effects of climate change on farm households, farm productivity and farm profitability through adaptation strategies. Consequently, the agricultural sector of developing countries like India is being restructured, reformed and realigned to contextualize the climate change-sustainable agriculture-farm livelihood nexus. Our exhaustive literature review exhorts a framework of how various types of CSA interventions (scientific technologies, indigenous technical knowledge, institutional innovations and information and communication technologies) can help to promote sustainable livelihood outcomes. The implementation of this approach is driven by the livelihood status of various strata of farmers, along with their vulnerability profile, resilience capacity and climate knowledge with regards to contrasting rationales of climatic vagaries. Climate change is a global process with local visibility; in countries that are dependent on an agrarian economy, a balanced mix of adaptation mechanisms to de-risk the vulnerable farm livelihoods and re-route them towards smart interventions can be important for climate-proofing agriculture. The above mentioned framework provides a robust future course of action for circumventing adverse climatic impacts.

No abstract

We consider equations in the modified Korteweg-de Vries (mKdV) hierarchy and make use of the Miura transformation to construct expressions for their Lax pair. We derive a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV equations. We also show that the complex modified KdV (cmKdV) equation follows from the action principle to have a Lagrangian representation. This representation not only provides a basis to write the cmKdV equation in the canonical form endowed with an appropriate Poisson structure but also help to construct a semianalytical solution of it. The solution obtained by us may serve as a useful guide for purely numerical routines which are currently being used to solve the cmKdV equation

No abstract