Mathabhanga College, established in 1969, is one of the oldest college in Mathabhanga. It offers undergraduate courses in arts, commerce and sciences. The campus is in the Cooch Behar district. It is affiliated to Cooch Behar Panchanan Barma University.
In this article, we investigate the (2+1)-dimensional damping forcing coupled Burgers equation, which is obtain by adding damping and forcing terms from couple Burgers equation. The Lax pair of the (2+1)-dimensional damping forcing coupled Burgers equation is established. With the help of Lax pair, we derive the N-fold Darboux transformation of (2+1)-dimensional damping forcing coupled Burgers equation. Using one fold and two fold Darboux transformation, we demonstrated some wave solutions including solitary wave solution and periodic wave solution. The impact of damping and forcing terms in solitary wave solution and periodic solution is graphically demonstrated.
Groundwater degradation poses a critical threat to water security in the Indian subcontinent, driven by intensifying anthropogenic pressures and geogenic processes. This study conducts a comprehensive comparative assessment of spatial groundwater quality dynamics between the agriculturally intensive Ganga River Basin (GRB) and the ecologically distinct Brahmaputra River Basin (BRB). Utilizing 2325 samples from the Central Groundwater Board (2018), the analysis integrated the Water Quality Index (WQI), Inverse Distance Weighting (IDW), and Welch’s t-test across 12 key parameters (pH, EC, TH, Calcium, Mg, Cl, Bicarbonate, Sulphate, NO3, Fluoride, and Na). Results reveal profound, statistically significant disparities: the GRB faces widespread degradation, with 14.62
Tea industry plays a pivotal role for the sustainable development of Norther part of West Bengal. North Bengal is famous for 3Ts comprising Tea, Timber and Tourism. It is one of the important agro-based industries not only in West Bengal but also in India. The Sub-Himalayan North Bengal comprised of eight districts, namely Darjeeling, Jalpaiguri, Cooch Behar, Alipurduar, Kalimpong, Uttar Dinajpur, Dakshin Dinajpur and Malda and it is internationally renowned for its tea plantations, mainly Darjeeling tea, which enjoys Geographical Indication (GI) status. The present study is descriptive in nature and is based entirely on secondary data collected from Tea Board of India, Annual Report, reputed journals, articles and books etc. The objectives of the study are to examine history and growth of tea industry in North Bengal, its problems and prospects and suggests some policies measures. It also analyses spatial disparities using descriptive statistics such as mean, median, Range, standard deviation, and coefficient of variation. The findings of the study reveal a significant regional concentration of tea gardens in the Jalpaiguri and Darjeeling districts, along with significant inequalities in distribution and productivity. The study revealed that sustainable practices like economic sustainability, worker welfare, and market expansion can ensure sustainability of the tea industry in North Bengal. Effective policy intervention and cooperation among stakeholders are essential for energizing the industry.
A partial differential equation (PDE)-based approach combines soliton theory with data-driven and physics-constrained training to probe solitary wave dynamics and shoaling-induced amplification. A comparison of two advanced deep learning approaches, fully connected neural networks (FCNs) and physics-informed neural networks (PINNs), demonstrates distinct trade-offs among predictive accuracy, computational efficiency, and physical consistency. By explicitly incorporating governing physical laws into the training process, Such PINNs impose governing physical constraints that markedly improve extrapolation at significantly higher cost, where FCNs have superior accuracy and computational efficiency. These findings provide practical criteria for selecting appropriate deep learning strategies for complex wave modeling applications. From a geophysical perspective, the variable-coefficient KdV equation is employed as an idealized surrogate to expose bathymetry-driven shoaling and nonlinear energy focusing in tsunami-like wave evolution. The results further reinforce the established physical understanding that variations in bathymetric amplitude and abrupt topographic changes strongly influence wave generation, propagation, and amplification in deep-ocean environments. Overall, the findings position physics-aware deep learning as a decisive and scalable paradigm for physically grounded environmental wave analysis and predictive modeling.
A dissipative dust ion-acoustic wave model in a multicomponent collisional dusty plasma is investigated to clarify how ionization processes and collisional damping reshape solitary, periodic, and shock structures supported by dust ion-acoustic modes. The plasma configuration consists of inertial negatively charged dust grains, inertial positively charged ions, and inertialess superthermal electrons and positrons embedded in a neutral background, so that both dispersive and dissipative effects arise naturally from charge separation and from ionization, ion-neutral, ion-dust, and dust-neutral collisions. Within this framework, a reductive perturbation technique (RPT) is employed to derive, first, a damped Korteweg-de Vries (dKdV) equation away from critical compositions and, second, a damped modified Korteweg-de Vries (dmKdV) equation at critical regimes where the quadratic nonlinearity vanishes, and the cubic nonlinearity becomes dominant. Semi-analytical dissipative periodic and solitary solutions to the dKdV equation are constructed by combining known cnoidal and solitary KdV profiles with a time-dependent amplitude-width ansatz, while weighted residual methods are applied systematically to obtain approximate solitary and shock solutions of the dmKdV equation, allowing the soliton or shock parameters to evolve under weak damping. The parametric analysis demonstrates that compressive and rarefactive dust ion-acoustic structures coexist in distinct regions of the space of superthermality, temperature ratios, and compositional parameters; in particular, increasing the spectral index and the electron-positron temperature ratio tends to favor compressive modes and suppress rarefactive ones. It is further shown that collisional damping (via ion-dust and ion-neutral frequencies) and ionization-loss parameters lead to a systematic reduction of the amplitudes of periodic, solitary, and shock waves. Overall, the study provides a unified analytical description of dissipative dust ion-acoustic solitons, cnoidal waves, and shocks governed by damped KdV-type equations, and delineates the parameter domains in which each structure can exist and remain dynamically robust in realistic collisional dusty plasmas with superthermal light species.
