A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generalized Darboux transformation with arbitrary functions in time $t$ for the mKPESCS which, in contrast with the Darboux transformation for the mKP equation, provides a non-auto-B\"{a}cklund transformation between two mKPESCSs with different degrees. The formula for $n$-times repeated generalized Darboux transformation is proposed and enables us to find the rational solutions (including the lump solutions), soliton solutions and the solutions of breather type of the mKPESCS.Comment: 23 pages, no figures. to appeare in Physica

Soliton Resonances for MKP-II

Using the second flow - the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota's bilinear representation for both flows and combine them together as the bilinear system for MKP-II. Using this bilinear form we find one and two soliton solutions for the MKP-II. For special values of parameters our solution shows resonance behaviour with creation of four virtual solitons. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.Comment: 11 pages, 2 figures, Talk on International Conference "Nonlinear Physics. Theory and Experiment. III", 24 June-3 July, 2004, Gallipoli(Lecce), Ital

Coupled Modified KP Hierarchy and Its Dispersionless Limit

We define the coupled modified KP hierarchy and its dispersionless limit. This integrable hierarchy is a generalization of the ''half'' of the Toda lattice hierarchy as well as an extension of the mKP hierarchy. The solutions are parametrized by a fibered flag manifold. The dispersionless counterpart interpolates several versions of dispersionless mKP hierarchy.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Analisis Permintaan Minyak Kayu Putih oleh Rumah Tangga Berdasarkan Volume Penjualan Apotek Studi Kasus Sukabumi, Jawa Barat

Untuk meningkatkan peranan minyak kayu putih (MKP) dalam perekonomian nasional diperlukan upaya-upaya perbaikan sistem komoditas MKP mulai dari produksi hingga pemasaran. Terbatasnya informasi ekonomi dan pasar MKP menyulitkan dalam membuat prioritas strategi perbaikannya. Salah satu permasalahannya adalah apakah kondisi permintaan pasar MKP memungkinkan upaya pengembangannya. Sebagai studi kasus, penelitian ini bertujuan untuk mengkaji permintaan MKP oleh rumah tangga berdasarkan pada volume penjualan apotek di Sukabumi, Jawa Barat. Hasil studi menunjukkan rerata permintaan MKP oleh rumah tangga per bulan adalah 39 botol setara dengan 2.201 ml, yang berarti satu jenis ukuran dan merk dagang berpeluang dibeli per bulan oleh rumah tangga sebanyak 39 botol setara dengan 2.201 ml. Dua belas jenis ukuran dan sembilan merk dagang memperebutkan peluang pasar tersebut. Ukuran botol yang mendominasi permintaan oleh rumah tangga adalah ukuran 15 ml, 30 ml, 60 ml dan 120 ml dan masing-masing ukuran didominasi oleh merk Caplang, Sidola, Dragon dan Konicare. Harganya berkisar antara Rp 91,63 hingga Rp 227,50 per ml. Menggunakan model persamaan regresi linier berganda, hasil studi menunjukkan harga MKP dan promosi MKP di TV mempengaruhi permintaan MKP oleh rumah tangga secara signifikan. Nilai elastisitas harga MKP cenderung lebih besar dari satu, yang berarti jika harga MKP meningkat atau menurun sebesar 1%, maka permintaan MKP oleh rumah tangga per bulan dapat diharapkan menurun atau meningkat dengan jumlah yang lebih besar yang mana dalam kasus Sukabumi sebesar 1,71%. Promosi MKP di TV yang secara signifikan berhubungan positif mengindikasikan bahwa permintaan MKP oleh rumah tangga per bulan dapat diharapkan meningkat dengan adanya promosi yang mana dalam kasus Sukabumi sebesar 3.372 ml

Model-independent evidence for J/ψpJ/\psi p contributions to Λb0→J/ψpK−\Lambda_b^0\to J/\psi p K^- decays

The data sample of $\Lambda_b^0\to J/\psi p K^-$ decays acquired with the LHCb detector from 7 and 8~TeV $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$, is inspected for the presence of $J/\psi p$ or $J/\psi K^-$ contributions with minimal assumptions about $K^- p$ contributions. It is demonstrated at more than 9 standard deviations that $\Lambda_b^0\to J/\psi p K^-$ decays cannot be described with $K^- p$ contributions alone, and that $J/\psi p$ contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for $P_c^+\to J/\psi p$ charmonium-pentaquark states in the same data sample.Comment: 21 pages, 12 figures (including the supplemental section added at the end